The dimensions of a metallic cuboid are 50 cm × 40 cm × 32 cm. This cuboid is melted and recast into a cube. Find the surface area of the cube.

Correct option is D

Given:

Dimensions of the cuboid: 50 cm × 40 cm × 32 cm

The cuboid is melted and recast into a cube.

Concept Used:

The volume remains the same when an object is melted and recast.

Formula Used:

Volume of cuboid: V=length× breadth × height

Volume of cube: V =$$a^3$$​ (where a is the side of the cube)

Surface area of the cube: S =$$6a^2$$​​

Solution:

V =$$50 \times 40 \times 32 = 64000 \text{ cm}^3$$​​

​$$a^3 = 64000$$​​

a=40 cm

S =$$6 \times (40)^2$$​​

= $$6 \times 1600$$​​

= $$9600 \text{ cm}^2$$

Option (D) is right.