SOLID FIGURESOLID FIGURE

• CUBE CUBE • CUBOIDCUBOID. PRISM. PRISM

. PYRAMID. PYRAMID

CUBE

A

H

E F

D C

B

G

ss

s

S = edge

face

AC = face diagonalCE = space diagonalACGE = diagonal plane

A

H

E F

D C

B

G

ss

s S = edge

face

AC = face diagonalCE = space diagonalACGE = diagonal plane

CUBOID

A

H

E F

DC

B

G

l

h

w

h

l

AG= space diagonal

ABGH= plane of diagonal

VOLUME OF A CUBEEach cube has equal edgeslength = width = height, Then the volume of a cube:Volume = edge x edge x edgeIf s = edge of a cubeWe getVolume = S x S x S = S3 Hence V = S3

A

H

E F

D C

B

G

SURFACE AREA OF A CUBE

Each cube consist of 6 squared faces which have equal area.

Area = 6 x S x S

= 6 S2

So, A = 6 S2

A

H

E F

D C

B

G

S

S

S

VOLUME OF A CUBOIDEach cuboid has: length (l), width (w) and height (h).

Volume = l x w x h = lwh

So, V = lwhA

H

E F

D C

B

G

SURFACE AREA OF A CUBOID

A1 = 2 x l x w

A2 = 2 x l x h

A3 = 2 x w x h

A

H

E F

D C

B

G

SURFACE AREA OF A CUBOID

Surface area of a cuboid:

Area = A1 + A2 + A3

= 2lw + 2lh + 2wh = 2 (lw + lh + wh)

A

H

E F

D C

B

G

EXAMPLE 1

Calculate the volume and the surface area of a cube whose the length of the edges is as the following:

a. 6 cm

b. 10 cm

c. 15 cm

d. 20 cm.

SOLUTION

a. S = 6 cm.

V = S3

= 6 x 6 x 6

= 216 cm3

A = 6 S2

= 6 x 6 x 6

= 216 cm2

SOLUTION

b. S = 10 cm.

V = S3

= 10 x 10 x 10

= 1.000 cm3

A = 6 S2

= 6 x 10 x 10

= 600 cm2

SOLUTIONc. S = 15 cm.

V = S3

= 15 x 15 x 15

= 3.375 cm3

A = 6 S2

= 6 x 15 x 15

= 1.350 cm2

SOLUTION

d. S = 6 cm.

V = S3

= 20 x 20 x 20

= 8.000 cm3

A = 6 S2

= 6 x 20 x 20

= 2.400 cm2

EXAMPLE 2

Calculate the volume and the surface area of a cuboid whose the length of the edges:a. l = 12 cm, w = 8 cm, h = 6 cm

b. l = 15 cm, w = 12 cm, h = 8 cm

SOLUTION

a. l = 12 cm, w = 8 cm, h = 6 cm V = l . w . h = 12 x 8 x 6 = 576 cm3 A = 2 (lw + lh + wh) = 2 (12 x 8 + 12 x 6 + 8 x 6) = 2 (96 + 72 + 48) = 2 x (216) = 432 cm2

SOLUTIONb. l = 15 cm. w = 12 cm, h = 8 cm

V = l . w . h

= 15 x 12 x 8

= 1.440 cm3

A = 2 (lw + lh + wh)

= 2 (15 x 12 + 15 x 8 + 12 x 8)

= 2 (180 + 120 + 96) = 2 x (396)

= 792 cm2

EXERCISE - 1

Calculate the volume of a cuboid whose height is 20 cm and the base is in the form of a square whose side is 7 cm long

Solution

Given : the length of its base = 7 cm

height = 20 cm

Volume = Base area x height

= (7 cm x 7 cm) x 20 cm

= 980 cm3

So, the volume of the cuboid is 980 cm3.

EXERCISE - 2

Calculate the volume and the surface area of a cube whose face diagonal is cm 24

Solution

Given:Face diagonal = cm

then The length of the edge = 4

V = 43

V = 64So, the volume of the cube is 64 cm3

24

Solution

Given:Face diagonal = cm

then The length of the edge = 4

A = 6 x 4 x 4V = 96

So, the surface area of the cube is 96 cm3

24