III Year Area Surface and Volume Module

8/12/2019 III Year Area Surface and Volume Module

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Aptitude and Reasoning Course Area, Surface area and

Volume

SITAMS, Chittoor Page 1

CALCULATION OF AREA,SURFACE AREA AND VOLUME


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A. Module Objective

This Module describes various standard geometrical structures that exist and

methods/formulas for calculating its characteristic values that can be used for various

applications/calculations. The structures include circle, triangle, cylinder etc., that exists with

in or as a shape, in all the practical entities we see in our daily life. So, calculating its area,

Volume and perimeter gives the mathematical insight about the structure.

For example, in order to determine the number of tiles of specific shape to be placed

over the floor of specific dimension, area of both tile and the floor become the basis.

B. Prerequisites (Related Formulas):-

1. Area Calculations: Area is a quantity that expresses the extent of a two-

dimensional surface or shape in the plane. Area can be understood as the amount of

material with a given thickness that would be necessary to fashion a model of the

shape, or the amount of paint necessary to cover the surface with a single coat.

1 square kilometer = 1,000,000 square meters,

1 square meter = 10,000 square centimetres = 1,000,000 square millimeters

1 square centimetre = 100 square millimeters

1 square yard = 9 square feet

1 square mile = 3,097,600 square yards = 27,878,400 square feet

a. square = a2

b. rectangle = ab

c. parallelogram = bh

d. trapezoid = h/2 (b1 + b2)

e. circle =pi r2

f. ellipse =pi r1 r2


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g. triangle =

h. equilateral triangle

i. triangle given a,b,c = [s(s-a)(s-b)(s-c)] where

s = (a+b+c)/2 (Heron's formula)

j. isosceles triangle = (b/4)*((4a2-b2))

k.regular hexagon = (33/2)*a

2

where a is its side

l. rhombus = 0.5*diagonal 1 * diagonal 2

m.

2. Volume Calculations: Volume is the quantity of three-

dimensional space enclosed by some closed boundary, for example, the space that

a substance (solid, liquid, gas, or plasma) or shape occupies or contains.[1]

Volume

is often quantified numerically using the SI derived unit, the cubic metre.

1 litre = (10 cm)3

= 1000 cubic centimetres = 0.001 cubic metres,1 cubic metre = 1000 litres.

Small amounts of liquid are often measured in millilitres,

where 1 millilitre = 0.001 litres = 1 cubic centimetre.

a. cube = a 3

b. rectangular prism = a b c

c. irregular prism = b h

d. cylinder = b h =pi r 2 h

e. pyramid = (1/3) b h


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f. cone = (1/3) b h = 1/3pi r 2 h

g. sphere = (4/3)pi r 3

h. ellipsoid = (4/3)pi r1 r2 r3

3. Surface Area Calculations: Surface area is the measure of how much exposed

area a solid object has, expressed in square units. Mathematical description of the

surface area is considerably more involved than the definition of arc length of a

curve.

a. Surface Area of a Cube = 6 a2

(a is the length of the side ofeach edge of the cube).

In words, the surface area of a cube is the area of the six squares that

cover it. The area of one of them is a*a, or a2

. Since these are all the same,

you can multiply one of them by six, so the surface area of a cube is 6 times

one of the sides squared.

b. Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac

(a, b, and c are the lengths of the 3 sides).

In words, the surface area of a rectangular prism is the area of the six

rectangles that cover it. But we don't have to figure out all six because we know

that the top and bottom are the same, the front and back are the same, and the left

and right sides are the same.

The area of the top and bottom (side lengths a and c) = a*c. Since there are

two of them, you get 2ac. The front and back have side lengths of b and c. The

area of one of them is b*c, and there are two of them, so the surface area of those

two is 2bc. The left and right side have side lengths of a and b, so the surface area

of one of them is a*b. Again, there are two of them, so their combined surface

area is 2ab.

c. Surface Area of Any Prism (b is the shape of the ends)

Surface Area = Lateral area + Area of two ends

(Lateral area) = (perimeter of shape b) * L


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Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)

d. Surface Area of a Sphere = 4pi r2

(r is radius of circle)

e. Surface Area of a Cylinder = 2 pi r2

+ 2 pi r h (h is the height

of the cylinder, r is the radius of the top)

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r2) + (2pi r)* h

In words, the easiest way is to think of a can. The surface area is the areas of

all the parts needed to cover the can. That's the top, the bottom, and the paperlabel that wraps around the middle. You can find the area of the top (or the

bottom). That's the formula for area of a circle (pi r2).

Since there is both a top and a bottom, that gets multiplied by two. The side is

like the label of the can. If you peel it off and lay it flat it will be a rectangle. The

area of a rectangle is the product of the two sides. One side is the height of the

can, the other side is the perimeter of the circle, since the label wraps once around

the can.

So the area of the rectangle is (2pi r)* h. Add those two parts together and you

have the formula for the surface area of a cylinder.

4. Perimeter Calculations: A perimeter is a path that surrounds an area. The word

comes from the Greekperi (around) andmeter(measure). The term may be used

either for the path or its length - it can be thought of as the length of the outline of

a shape.

a. square = 4a

b. rectangle = 2a + 2b

c. triangle = a + b + c

d. circle =2pi r

circle =pi d (where d is the diameter). The perimeter of a circle is more

commonly known as the circumference.


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Properties of various Geometrical structures:

a. Triangle

In an equilateral triangle all sides have the same length. An equilateral triangle is also

a regular polygon with all angles measuring 60.

In an isosceles triangle, two sides are equal in length. An isosceles triangle also has

two angles of the same measure; namely, the angles opposite to the two sides of the same

length; this fact is the content of the Isosceles triangle theorem.

In a scalene triangle, all sides are unequal. The three angles are also all different in

measure. Some (but not all) scalene triangles are also right triangles.

A right triangle (or right-angled triangle, formerly called a rectangled triangle) has

one of its interior angles measuring 90 (a right angle). The side opposite to the right angle isthe hypotenuse; it is the longest side of the right triangle. The other two sides are called

thelegs of the triangle.

Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of

the two legs is equal to the square of the length of the hypotenuse: a2

+b2

=c2,

wherea andb are the lengths of the legs andc is the length of the hypotenuse.

Triangles that do not have an angle that measures 90 are called oblique triangles.

A triangle that has all interior angles measuring less than 90 is an acute

triangle or acute-angled triangle.

A triangle that has one angle that measures more than 90 is an obtuse

triangle or obtuse-angled triangle.

A "triangle" with an interior angle of 180 (and collinear vertices) is degenerate.

b. Quadrilateral

In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or 'edges')

and four vertices or corners. Sometimes, the term quadrangle is used, by analogy

with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-

sided) and so on. The word quadrilateral is made of the wordsquad (meaning "four")

and lateral (meaning "of sides").

The diagonals of parallelogram bisect each other

Each diagonal of a parallelogram divides it into two triangles of the same area

The diagonals of rectangle are equal and bisect each other


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The diagonals of square are equal and bisect each other at right angles

The diagonals of rhombus are unequal and bisect each other at right angles

c. Circle

The circle is the shape with the largest area for a given length of perimeter.

A circle's circumference and radius are proportional.

The area enclosed and the square of its radius are proportional.

The constants of proportionality are 2 and , respectively.

The circle which is centered at the origin with radius 1 is called the unit circle.

Some Important Metrics:

1. 10,000 sq meters = 1 hectare

2. 100 hectares = 1 sq kilo meter

3. 1000 millimeters = 1 meter

4. 100 centimeters = 1 meter

5. 1000 metres = 1 kilometer

6. 1000 kilograms = 1 mega gram or 1 tonne

7. 3.6 kilometers per hour = 1 meter per second

8. 3600 kilometers per hour = 1 kilometer per second

C. Solved Examples

1. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling

along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes,

then the area of the park (in sq. m) is:

A.15360 B.153600

C.30720 D.307200

Answer & Explanation

Answer:Option

B

Explanation:

Perimeter = Distance covered in 8 min. =12000

x 8m = 1600 m.60

Let length = 3x metres and breadth = 2x metres.


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Then, 2(3x + 2x) = 1600 orx = 160.

Length = 480 m and Breadth = 320 m.

Area = (480 x 320) m2

= 153600 m2.

2. An error 2% in excess is made while measuring the side of a square. The percentage of

error in the calculated area of the square is:

A.2% B.2.02%

C.4% D.4.04%


Answer: OptionD

Explanation:

100 cm is read as 102 cm.

A1 = (100 x 100) cm2

and A2 (102 x 102) cm2.

(A2 - A1) = [(102)2

- (100)2]

= (102 + 100) x (102 - 100)

= 404 cm2.

Percentage error =

404

x 100 %= 4.04%100 x 100

3. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the

rectangle is 216 sq. cm, what is the length of the rectangle?

A.16 cm B.18 cm

C.24 cm D.Data inadequate

E.None of these


Answer: OptionB

Explanation:

2(l +b)=

5

b 1

2l + 2b = 5b

3b = 2l


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b =2

l3

Then, Area = 216 cm2

l xb = 216

l x2

l= 2163

l2

= 324

l = 18 cm.

4. The percentage increase in the area of a rectangle, if each of its sides is increased by 20%

is:

A.40% B.42%C.44% D.46%


Answer: OptionC

Explanation:

Let original length =x metres and original breadth =y metres.

Original area = (xy) m2.

New length =120

xm

=6

m.100 5

New breadth =120

ym

=6y

m.100 5

New Area =6x x

6y

m2=

36xy

m2.5 5 25

The difference between the original area = xy and new-area 36/25 xy is

= (36/25)xy - xy

= xy(36/25 - 1)

= xy(11/25) or (11/25)xy

Increase % = 11 xy

x1 x 100

%= 44%.

5. A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the


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middle of the park and rest of the park has been used as a lawn. If the area of the lawn is

2109 sq. m, then what is the width of the road?

A.2.91 m B.3 m

C.5.82 m D.None of these


Answer: OptionB

Explanation:

Area of the park = (60 x 40) m2

= 2400 m2.

Area of the lawn = 2109 m2.

Area of the crossroads = (2400 - 2109) m2

= 291 m2.

Let the width of the road bex metres. Then,

60x + 40x -x2

= 291

x2

- 100x + 291 = 0

(x - 97)(x - 3) = 0

x = 3.

6. The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet

is 4 feet. What is the area of the closet in square feet?

A.51

4B.13

1

2

C.27 D.37


Answer: OptionC

Explanation:

Other side= 15 2- 9 22 2

ft

=225

-81

4 4ft

=144

4ft

=6 ft.

Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.


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7. A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth.

The percentage of decrease in area is:

A.10% B.10.08%

C.20% D.28%


Answer: OptionD

Explanation:

Let original length =x and original breadth =y.

Decrease in area=xy -80

xx90

y100 100

= xy -18

xy

25

=7

xy.25

Decrease % =7

xy x1

x 100%

= 28%.25 xy

8. A man walked diagonally across a square lot. Approximately, what was the

percent saved by not walking along the edges?


Answer: OptionC

Explanation:

Let the side of the square(ABCD) bex metres.

Then, AB + BC = 2x metres.

AC = 2x = (1.41x) m.

Saving on 2x metres = (0.59x) m.


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Saving % = 0.59xx 100%

= 30% (approx.)

9. The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the

rectangle must be:

A.9 cm B.18 cmC.20 cm D.41 cm


Answer: OptionB

Explanation:

l2

+b2

= 41.

Also,lb = 20.

(l +b)2

= (l2

+b2) + 2lb = 41 + 40 = 81

(l +b) = 9.

Perimeter = 2(l +b) = 18 cm.

10. What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm

long and 9 m 2 cm broad?

A.814 B.820

C.840 D.844


Answer: OptionA

Explanation:

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.

Area of each tile = (41 x 41) cm2.

Required number of tiles =1517 x 902

= 814.

41 x 41

11. The difference between the length and breadth of a rectangle is 23 m. If its perimeter

is 206 m, then its area is:

A.1520 m2

B.2420 m2

C.2480 m2

D.2520 m2



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Answer: OptionD

Explanation:

We have: (l -b) = 23 and 2(l +b) = 206 or (l +b) = 103.

Solving the two equations, we get:l = 63 andb = 40.

Area = (l xb) = (63 x 40) m2

= 2520 m2.

12. The length of a rectangle is halved, while its breadth is tripled. What is the percentage

change in area?

A.25% increase B.50% increase

C.50% decrease D.75% decrease


Answer: OptionB

Explanation:

Let original length =x and original breadth =y.

Original area =xy.

New length =x

.2

New breadth = 3y.

New area = x

x 3y =3xy.

2 2

Increase % = 1xy x1x 100%

= 50%.

13. The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing

the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

A.40 B.50

C.120 D.Data inadequateE.None of these


Answer: OptionE

Explanation:


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Let breadth =x metres.

Then, length = (x + 20) metres.

Perimeter =5300

m = 200 m.26.50

2[(x + 20) +x] = 200

2x + 20 = 100

2x = 80

x = 40.

Hence, length =x + 20 = 60 m.

14. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If

the area of the field is 680 sq. feet, how many feet of fencing will be required?

A.34 B.40

C.68 D.88


Answer: OptionD

Explanation:

We have:l = 20 ft andlb = 680 sq. ft.

So,b = 34 ft.

Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.

15. A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom

at 75 paise per sq. m, is:

A.Rs. 456 B.Rs. 458

C.Rs. 558 D.Rs. 568


Answer: OptionC

Explanation:

Area to be plastered= [2(l +b) xh] + (l xb)


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= {[2(25 + 12) x 6] + (25 x 12)} m2

= (444 + 300) m2

= 744 m2.

Cost of plastering = Rs. 744 x75

= Rs. 558.100

D. Exercise Problems

1. A regular hexagon is inscribed in a circle of radius 8 cm. Find the area in circle other than

hexagon portion

a)6(2 -3) b)3(2 -3)c)18(2 -3) d)none

2. Find the area of a rhombus one side of which measures 15cm and one diagonal is 24cm?

a)512 cm b)216 cm

c)450 cm d) 309 cm

3. Find the area of an isosceles triangle whose equal sides are 8cm each and the third side is

10cm?a)10 cm b)48 cm

c)539 cm d)1010 cm

4. A rope 88m long has been bent in the form of a circle. Find the area of the circle?

a)343 m b)616 m

c)196 m d)225 m

5. The area of a circle is 220sq.cm.What will the area of a square inscribed in this circle will

be?

a)110 cm b)120 cm

c)140 cm d)160 cm

6. From a solid right circular cylinder with a height of 10cm and a diameter of the base of

12cm,a right circular cone of the same height and base is cut off. Find the remaining volume

of solid?

a)624.6 cm3

b)616 cm3

c)728.6 cm3

d)754.28 cm3

7. A hollow spherical shell is made of metal of density 4.8g/ cm3.

If its internal and external radii are 10cm and 12cm respectively, find the weight of the shell

a)15.24kg b)12.84kg

c)14.64kg d)none

8. If the average distance of the sun from the earth is 91 x 106

miles and the angles subtended

by the sun at the edge of a person on the earth is 3 minutes, the diameter of the sun in miles is

approximately

a)85000 b)632000

c)73333 d)793722


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9. Ramu has bought a field in the shape of a parallelogram with a perimeter of 320m and one

internal angle=1500.If he wants to utilize the maximum area for cultivation ,what should be

the length of his field?

a)70,90 b)80,80

c)75,85 d)cannot be computed

10. The front wheels of a cart cover a distance of 3 m in one revolution and the rear wheelscover a distance of 4m in one revolution.What will be the distance traveled by the cartwhen the front wheels have made 5 more revolution than the rear ones?

a)20 b)15

c)100 d)5

11. A rectangular carpet has an area of 240 sq.metres.If its diagonal and the longer side

together are equal to five times the shorter side,what will be the length of the carpet?

a)5m b)10m

c)12m d)24m

12. If the ratio of the areas of two squares is 16:1, What will be the ratio of their perimeter?a)1:16 b)1:4

c)4:1 d)8:1

13. The length of a rectangle is 1 cm more than its breadth .its perimeter is 14cm.What will

be the area of the rectangle?

a)4 cm b)3 cm

c)6 cm d)12 cm

14. If the side of an equilateral triangle is decreased by 20%,its area is decreased by what

percent?

a)20% b)25%

c)36% d)40%

15. If the radius of a circle is doubled,by how much percentage does the area increases?

a)100% b)200%

c)300% d)400%

16. Find the volume of a cube whose surface area is 384sq.cm?

a)343 cm3

b)384 cm3

c)400 cm3

d)512 cm3

17. The slant height of the frustum of a cone is 20cm and the height of the frustum is 16cm

.the radius of the smaller circle is 8cm.find the volume of the frustum?

a)9880 cm3 b)10459.43 cm3

c)11960 cm3

d)12464 cm3

18. What is the total surface area of a cylinder that has been made from a rectangle of length

12m & breadth 10m?

a)120 m b)132 m

c)120+25/ m d)none

19. Triangle ABC is right angled at C.What is the value of


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tan A + tan B?

a)a+b b)c/ab

c)a/bc d)b/ac

20. A rectangle plot has to be fenced on one long side ,one short side and the diagonal.If the

cost of fencing is Rs.5per metre ,the area of the plot is 1,200 sq.m. and the short side is 30m

long,how much would be the job cost?

a)Rs.300 b)400

c)500 d)600

21. A man walks at the rate of 6km/hr and crosses a square field diagonally in 9 seconds

.What is the area of the field?

a)81m b)112.5m

c)121m d)125m

22. The ratio of the length and breadth of a rectangular park is 3:2.A man cycles along the

boundary of the park at a speed of 12km/hr and completes one round in 8min .find the area ofthe park.

a)143200m b)137900m

c)78300m d)153600m

23. A room is 13m long ,9 m broad and 10m high .Find the cost of painting the four walls of

the room at Rs.6 per.sq.m .The doors and windows occupy 32sq.m?

a)Rs.1331 b)1225

c)2448 d)3000

24. A rectangular lawn 45m by 35m has two roads each 5m wide running in the middle of it,

one parallel to length and the other parallel to the breadth. Find the cost of repairing them at

rs.1 per sq.m?a)Rs.225 b)300

c)375 d)400

25. A field is in the form of a trapezium whose parallel sides are 110m and 65m and the

height between the two parallel side is 56 am.Find the cost of ploughing the field at the rate

of 70paise per sq.m?

a)Rs.2250 b)1525

c)3430 d)5120

26. ABCD is a quadrilateral where in AC is 15cm . The length of the perpendicular from D

and B on AC are 5cm and 7cm respectively.What will the area of the quadrilateral be?

a)90cm b)180cmc)225cm d)45cm

27. An equilateral triangle of side 6cm has its corners cut off to form a regular hexagon .What

will be the area of the hexagon?

a)93cm b)63cmc)33cm d) 3cm


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28. A circular grassy land has a path 7m wide running round it on the outside. The radius of

the land is 35m.how many stones of dimensions 20cm x 11cm are required to prove the path?

a)7000 b)11000

c)77000 d)10000

29. The area of the circle circumscribed by a regular hexagon is 2. What is the area of thehexagon?

a)93cm b)63cmc)33cm d) 3cm

30. The minute hand of a clock is 7cm long.What will the area swept by the minute hand in

15minutes be?

a)19.25 cm b)38.5 cm

c)77 cm d)none

31. A powder tin has a square base with sides of 8cm and height 14cm.another powder tin has

a circular base with a diameter of 8cm and height 14cm.find the difference in their capacities?

a)93cm b)63cmc)33cm d) None

32. A large field of 700 hectares is divided in to two parts. The difference of the areas of the

two parts in one-fifth of the average of the two areas. What is the area of the smaller part in

hectages?

a)225 b)280

c)300 d)315

33. A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm foreach part folded along one set of sides and the same in 38 cm when folded along the other set

of sides. What is the area of the paper in sq. cm

a)140 b)240

c)540 d)None

34. The cost of carpeting a room 18m long with a carpet 75 cm wide at Rs. 4.50 per metre is

Rs. 810. The breadth of the room is___mts.

a)7 b)7.5

c)8 d)8.5

35. A courtyard 25 cm long and 16 mts broad is to be paved with bricks of dimensions 20 cm

by 10 cm. The total number of bricks required is

a)18000 b)20000

c)25000 d)None

36. The length of a rectangle is 20% more than its breadth. What will be the ratio of the area

of a rectangle to that of a square whose side is equal to the breadth of the rectangle.


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a)2:1 b)5:6

c)6:5 d)None

37. A square and rectangle have equal areas. If their perimeters are p 1 and p2 respectively,

then

a)p1p2 d)None

38. The diagonal of a square is 42 cm. The diagonal of another square whose area is doublethat of the first square is ___ cm.

a)8 b) 82c) 42 d)16

39. A rectangular water tank is 80m X 40 m. Water flows into it through a pipe 40 sq.cm at

the opening at a speed of 10 km/hr. By how much, the water level will rise in the tank in half

an hour

a)3/2 cm b)4/9 cm

c)5/8 cm d)None

40. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is

equal to the sum of areas of the four walls, the volume of the hall is

a)720 b)900

c)1200 d)1800

41. The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 55 cm.Its surface area is___ sq. cm

a)125 b)236

c)361 d)486

42. What is the number of iron rods, each of length 7 mts and diameter 2 cm that can be made

out of 0.88 cubic metres of iron

a)100 b)200

c)300 d)400

43. A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deepon the deeper side. Its volume is___ mt. cube

a)208 b)270

c)360 d)408

44. The ratio of total surface area to lateral surface area of a cylinder whose radius is 20 cm

and height 60 cm is


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a)2:1 b)3:2

c)4:3 d)5:3

45. A powder tin has a square base with side 8 cm and height 14 cm. Another tin has a

circular base with diameter 8 cm and height 14 cm. The difference in their capacities is___

cu.cms

a)0 b)132

c)137.1 d)192

46. The ratio between the radius of the base and the height of a cylinder is 2:3. If its volume

is 12936 cu. Cm, the total surface area of the cylinder is____sq.cm

a)2587.2 b)3080

c)25872 d)38808

47. The radius of the cylinder is half its height and area of the inner part is 616 sq.cm.Approximately how many litres of milk can it contain

a)1.4 b)1.5

c)1.7 d)1.9

48. The sum of the radius of the base and height of a solid cylinder is 37 metres. If the total

surface area of the cylinder be 1628 sq.metres, it volume is

a)3180 b)4620

c)5240 d)None

49. Two cones have their heights in the ratio 1:3 and radii 3:1. The ratio of their volumes is

a)1:1 b)1:3

c)3:1 d)2:3

50. The radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their

heights

a)1:8 b)1:4

c)2:1 d)4:1


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SOLUTION TO EXERCISE PROBLEMS:


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E. Previous Exam Questions:

1.If the volume of a sphere is divided by its surface area, the result is 27 cm. The radius of the

sphere is___cm. [C.D.S. 2005]

a)9 cm b)36 cm

c)54 cm d)81 cm

2. Spheres A and B have their radii 40 cm and 10 cm respectively. The ratio of the surface

area of A to the surface area of B is: [Bank P.O. 2000]

a)1:4 b)1:16

c)4:1 d)16:1

3. Surface area of a sphere is 2464 sq. cm. If its radius be doubled, then the surface are of thenew sphere will be [Bank P.O. 2001]

a)20 b)15

c)100 d)5

4.If the radius of a sphere is doubled, how many times does its volume become

[S.S.C. 2000]

a)2 times b)4 times

c)6 times d)8 times

5.If the radius of a sphere is increased by 2 cm, then it surface area increases by 352 sq. cm.

The radius of the sphere before the increase was___ cm. [C.D.S.2006]

a)3 b)4

c)5 d)6

6.If the measured value of the radius is 1.5% larger, the percentage error (correct to one

decimer place) made in calculating the volume of a sphere is

[Bank P.O. 2003]

a)2.1 b)3.2

c)4.6 d)5.4

7.A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered

in to the water until it is completely immersed. The water level in the vessel will rise

by___cm.

[Infosys 2009]

a)2/9 b)4/9

c)9/4 d)9/2


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16.A rectangular room can be partitioned in to two equal square rooms by a partition 7 metres

long. What is the area of the rectangular room in square metres [Bank P.O. 2005]

a)49 b)147

c)196 d)None

17.The three sides of a triangle are 5cm, 12cm and 13 cm respectively. Then, its area

is___sq.cm

[S.S.C. 2000]

a)103 b)106c)20 d)30

18.The sides of a triangle are in the ratio of , 1/3, 1/4 . If the perimeter is 52 cm. Then the

length of the smallest side is____cm. [Bank P.O. 2004]

a)9 b)10

c)11 d)12

19.The area of a triangle is 216 sq.cm and its sides are in the ratio 3:4:5. The perimeter of the

triangle is___cm. [C.D.S. 2007]

a)49 b)12

c)35 d)72

20.The sides of a triangle are 3cm, 4 cm, and 5 cm. The area of the triangle formed by joining

the mid-points of the sides of this triangle is [C.D.S. 2006]

a)3/4 b)3/2

c)3 d)6

21. The slant height of a right circular cone is 10 mts and its height is 8 mts . Find the area of

its curved surface____sq.mts. [Bank P.O. 2005]

a)30 b)40c)60 d)80

22. If a right circular cone of height 24 cm has a volume of 1232 cu.cm, then the area of its

curved surface is___sq.cm [S.S.C. 2008]

a)154 b)550

c)704 d)1254

23.The curved surface of a right circular cone of height 15 cm and base diameter 16 cm

is___sq.cm [S.S.C. 2002]

a)60 b)68c)120 d)136


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24. If the volume of a sphere is divided by its surface area, the result is 27 cm. The radius of

the sphere is____cm. [C.D.S. 2005]

a)9 b)36

c)54 d)81

25. If the radius of a sphere is doubled, how many times does its volume become___times.

[S.S.C. 2005]

a)2 b)4

c)6 d)8

26. If the radius of a sphere is increased by 2 cm, then its surface area increases by 352

sq.cm. The radius of the sphere before the increase was___cm. [R.R.B.

2003]

a)3 b)4

c)5 d)6

27. There is a square of side 6 cm . A circle is inscribed inside the square. Find the ratio of

the area of circle to square. [Honey Well

2009]

a) /5 b) /4c) /6 d) /2

28. One rectangular plate with length 8inches,breadth 11 inches and 2 inches thickness is

there. What is the length of the circular rod with diameter 8 inches and equal to

volume of rectangular plate? [HCL

2010]

a)3.5 b)4.5c)5.5 d)6.5

29. If the length of the rectangle is reduced by 20% and breath is increased by 20 % what is

the net change in % [TCS 2010]

a)3 b)4

c)5 d)6

30. How many squares with sides 1/2 inch long are needed to cover a rectangle that is 4 feet

long & 6feet wide [Infosys

2010]

a) 24 b)96

c)3456 d)13824

31. A warehouse had a square floor with area 10,000 sq.meters. A rectangular addition was

built along one entire side of the warehouse that increased the floor by one-half as much as

the original floor. How many meters did the addition extend beyond the original buildings?


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[TCS 2011]

A)10 B)20

C)50 D)200

32. A rectangular tank 10" by 8" by 4" is filled with water. If all of the water is to be

transferred to cube-shaped tanks, each one 3 inches on a side, how many of these smallertanks are needed?

A. 9 B. 12 [Infosys 2011]

C. 16 D. 21

Key to Exercise Problems:-

1.d 2.b 3.c 4.b 5.c 6.d 7.c 8.d 9.b 10.a

11.d 12.c 13.d 14.c 15.c 16.d 17.b 18.d 19.b 20.d

21.b 22.d 23.c 24.c 25.c 26.a 27.b 28.c 29.c 30.b

31.a 32.d 33.a 34.a 35.b 36.c 37.a 38.a 39.c 40.c

41.b 42.d 43.b 44.c 45.d 46.b 47.b 48.b 49.c 50.b

Key to Previous Exam Questions:-

1.d 2.d 3.b 4.d 5.d 6.c 7.c 8.d 9.d 10.b

11.e 12.a 13.c 14.c 15.b 16.d 17.d 18.d 19.d 20.b

21.c 22.b 23.d 24.c 25.d 26.d 27.b 28.a 29.b 30.a

31.c 32.b

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III Year Area Surface and Volume Module

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