Question

A cube and cuboid has the same volume. The side of the cube is 8 cm .The length and breadth of the cuboid are 8cm and 4 cm , the height of the cuboid is

Answer 1

Height of the cuboid is 16 cm

Explanation:

Let l stand for the length of a side

Let b and h be the base and the height of the cuboid.

Vc is the volume of the cube

Vcb is the volume of the cuboid

Volume formulas:

Cube: Vc = l^3 all sides = 1

Cuboid: Vcb = b*l*h

Volumes:

l = 8 cm

Cube: Vc = 8^3 cm^3

Vc = 512 cm^3

Cuboid: Vcb = (8 cm)*(4 cm)*h

Vcb = 32h cm^2

We are told that Vc = Vcb

Vcb = 32h cm^2 = 512 cm^3

32h cm^2 = 512 cm^3

h = (512 cm^3)/(32 cm^2)

h = 16 cm

Height of the cuboid is 16 cm