Question

A solid pieces of metal cuboidal in shape with dimensions 24cm, 18cm and 4cm is recast into a cube calculate the lateral surface area of the cube

Answer 1

Volume of cuboidal metal
= 24 cm * 18cm* 4 cm
= 1728 cubic cm

volume will remains same as the same metal cuboidal is recast into cube.

Volume of cube = 1728 cubic cm

side of cube = cube root of 1728
= 12 cm

Lateral surface area = 4 * side*side
= 4 * 12 * 12
= 576 sq. cm

Answer 2

The lateral surface area of cube is 576 cm².

A solid piece of metal cuboidal in shape with dimension 24 cm × 18 cm × 4cm is recast into a cube.

We have to calculate the lateral surface area of the cube.

∵ A solid piece of cuboidal metal is recast into a cube.

∴ volume of cuboid = volume of cube

⇒Length × Width × height = (edge length)³

⇒24 cm × 18 cm × 4cm = (edge length)³

⇒1728 cm³ = (edge length)³

⇒(12 cm)³ = (edge length)³

⇒edge length = 12 cm

now the lateral surface area of the cube = 4 × (edge length)²

= 4 × (12 cm)²

= 4 × 144 cm²

= 576 cm²

Therefore the lateral surface area of cube is 576 cm².