Question

A piece of metal in the form of a cone of radius 3cm and height 7cm is melted and cast into a cube . Find the side of the cube .

Answer 1

Find the volume of the cone:

Volume = 1/3 πr²h

Volume = 1/3 π(3)²(7) = 66 cm³

Find the side of the cube:

Volume = side³

66 = side³

side = ∛66

side = 4.04 cm

Answer: The side of the cube is 4.04 cm

Answer 2

Given:

Cone,

Radius = 3 cm

Height = 7 cm

To find:

The side of the cube:

Solution:

To find the volume of the cone,

By formula,

Volume = 1 / 3 * π * ( Radius )^2 * Height

Substituting,

Volume = 1/3 * π * ( 3 )^2 ( 7 )

Volume = 66 cu.cm

To find the side of the cube,

Volume of the cube = ( Length of the side )^3

Since the cone is melted to form a cube,

66 = ( Length of the side )^3

( Length of the side ) = ∛66

Length of the side = 4.046 cm

Hence, the length of the cube is 4.046 cm