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Revision on Circles

Section A: For each question, four options are given. (10 marks)

1) Jamie has a piece of cardboard. She realised that she can only cut out a maximum

of 8 circles of diameter 7cm each from it. What is the dimension of the

cardboard?

(A) 77cm x 16cm

(B) 28cm x 11cm

(C) 30cm x 15cm

(D) 56cm x 28cm

2) The figure shows circles inside a square. Find the area of the unshaded part. .

(Take 𝜋 to be227⁄ )

3) The figure below is made up of a square and a circle of radius 7cm. What is the

area of the shaded part? Leave your answer in terms of 𝜋

4) A piece of wire is cut and bent as shown in the figure below to form the fencing of

one side of a garden. Find the length of the piece of wire used. (Take π to

be22⁄7)

(A) (49 𝜋 – 98) cm ²

(B) (98-49 𝜋) cm ²

(C) 49 𝜋 cm ²

(D) (14 𝜋 – 98) cm ²

(A) 55m

(B) 76m

(C) 110m

(D) 131m

(A) 42cm²

(B) 44cm²

(C) 168cm²

(D) 154cm²

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5) The figure below, not drawn to scale, is made up of a quadrant and a semi-circle.

Find the area of the figure. (Take π to be22⁄7)

6) In the figure below, O is the centre of the circle and the circumference of the

circle is the same as the perimeter of the square. What is the area of the square?

(Take π to be22⁄7)

7) The figure is made up of two quadrants of different sizes. What is the perimeter

of the figure? (Take π to be22⁄7)

8) The figure below is made up of 3 identical quadrants with radius 7cm. What is

the perimeter of the figure? Give your answer in terms of π

(A) 319cm²

(B) 462cm²

(C) 1386 cm²

(D) 66cm²

(A) 22 cm²

(B) 88cm²

(C) 484cm²

(D) 154cm²

(A) 33 cm

(B) 44cm

(C) 100cm

(D) 88cm

(A) 3634⁄ π cm

(B) 21 π cm

(C) 1012⁄ π + 14cm

(D) 21 π+ 14cm

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9) The figure below is made up of a three-quarter circle and a quadrant. X is the

centre of the circle. What is the perimeter of the figure? Leave your answer in

terms of π.

10) The following is made up of 3 identical quadrants. Find the perimeter of the

figure. (Take π to be22⁄7)

Section B

Questions 11 to 15 carry 1 mark each. Questions 16 -20 carry 2 marks each. Show your workings clearly in the space provided for each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. (15 marks)

11) Find the perimeter of the semi-circle shown below. . (Take 𝜋 to be227⁄ )

Ans:____________________

12) The radius of a circle is 35cm. Find its area. (Take 𝜋 to be227⁄ )

Ans: ____________________

(A) 9π cm

(B) 11 π cm

(C) (9 π + 4) cm

(D) (11 π + 2) cm

(A) 54cm

(B) 47 cm

(C) 33cm

(D) 61cm

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13) The figure below is made up of a quadrant and rectangle OPQR. Find the perimeter of the rectangle.

Ans: ___________________

14) The figure is not drawn to scale, W is the centre of two concentric circles. Give that WY is 5cm and WZ is 9cm, find the area of the shaded region. Give your answer in terms of 𝜋

Ans:______ ______________

15) The figure below shows a circle and a square OBCD. The area of the square is

256cm². What is the area of the shaded part? Give your answer in terms of π.

Ans: ____________________

W Y 5cm

m

Z

9cm

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16) In the figure below, ABCD is a rectangle measuring 16cm by 8cm. Two equal

quadrants are drawn from the midpoint Y. Find the perimeter of the shaded part.

Take 𝜋 to be 3.14)

Ans:______________________

17) A disc of diameter 21cm is rolled from point X to point Y. The disc makes 18

revolutions to reach p point Y. What is the distance travelled by the disc? Take 𝜋

to be 3.14)

Ans:_________________________

18) MNOP is a square within a quadrant OST. Find the length of the line NP in terms

of X.

Ans: _________________________

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19) The figure below is made up of a semi-circle and a right angled isosceles triangle

STU. SU =ST and the diameter of the circle is 14cm. Find the total area of the

shaded part.

Ans:__________________________

20) In the figure below, WXYZ is a rectangle with some quadrant in it. Use the

calculator value 𝜋 to find the total area of the shaded parts. Calculate your

answers to 2 decimals place.

Ans:____________________

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Section C

Show your working clearly in the space provided for each question and write the answer in the space provided. The number of marks available is shown in the brackets ( ) at the end of each questions or part questions. (36 marks)

21) The figure below is not drawn to scale. Line OP is 105 cm and it cuts through the centre

of all four circles. Find the perimeter of the figure. Take 22

7

O 105 cm P

Ans:______________________

22) The radius of a bicycle is 28cm. How many revolutions does it need to make to

cover a distance of 440m? (Take 𝜋 to be 227⁄ ) (3m)

Ans:____________________

23) The figure shows a circle in a square. The radius of the circle is 10 cm.

What is the total area of the shaded parts, in terms of ?

Ans:__________________

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24) The figure is made up of two identical big quadrants and two identical small

quadrants. The area of the small quadrant is 1 4⁄ of the big quadrant. The radius

of the big quadrant is 56cm. Find the perimeter of the figure. (Take 𝜋 to be 227⁄ )

(4m)

Ans: ______________________

25) The figure below shows two identical triangle inscribed in a three-quarter circle

with centre O. Given that the area of the total shaded of the triangles is 144cm².

Find the area of the unshaded part in three-quarter circle. (Take π to be

22⁄7)(4m)

Ans:____________________

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26) Figure A and B are made up of quadrants of similar radii. Find the difference in

the unshaded area between Figure and B. Take π to be 3.14 (4m)

Ans: ______________________

27) Louis made some identical circles by bending some thin copper wire as shown

below. The diameter of each circle is 14cm. The length of the thin wire is 5m. The

distance between the centres of 2 circles is 27cm. (Take 𝜋 to be 227⁄ )

(a) What is the length of the wire after the last circle? (3m)

(b) How many circles did she bend? (1m)

Ans: (a)_________________________

(b) _________________________

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28) Figure A below shows a circular tile that is partly painted red. Jane uses some of

these circular tiles in figure A to pace on a garden pavement shown in figure B.

Each tile of diameter 20 cm is in contact with those next to it.

(a) What fraction of the circular tile in figure A is painted red? (1m)

(b) Find the area of the pavement that is not covered by the red paint of the tiles.

Take 𝜋 to be 3.14 (4m)

Ans(a)________________________

Ans (b)________________________

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29) The figure below shows a circle with centre O and radius 56cm. Two semi-circle

and two quarter circles are drawn within the circle. Find the perimeter of the

shaded parts. (Take π to be 22

7 ) (5m)

Ans: ______________________

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30) The figure is made up of a right-angled triangle WXY and a semi-circle of radius

5.8cm. O is the centre of the circle and the area of the sector EOD is one-third the

area of the semi-circle. DW=WX=DY=7cm.

Using the calculator value of 𝜋, find

(a) The area of the shaded region, correct to 2 decimal place.(3m)

(b) The perimeter of the shaded region, correct to 2 decimal place. (2m)

Ans:(a)_____________________

Ans: (b) ____________________