Question

The dimensions of a metallic cuboid are: 100 cm x 80 cm x 64 cm. It is melted and recast into a cube. Find the surface area of the cube.​

Answer 1

Dimensions of cuboid

l = 100cm

b = 80cm

h = 64cm

Volume of cuboid = lbh

= (100×80×64)cm³

= 512000cm³

Volume of cube = Volume of cuboid

(side)³ = 512000cm³

side = 80cm

T.S.A. of cube = 6(side)2

= 6 (80)²cm²

= (6×6400)cm²

= 38400cm²

Answer 2

solution:-

Volume of the metallic cuboid

= 100 x 80 x 64 cm

= 51200 cm^3

Since the metallic cuboid is melted and is recasted into a cube

Volume of the metallic cuboid = Volume of the cube.

Let the length of each edge of the recasted cube be a cm. Then,

Volume of the cube = Volume of the cuboid

${a}^{3} = 512000 \\ {a}^{3} = {8}^{3} \times {10}^{3} \\ a = 8 \times 10cm = 80cm$

therefore, surface area or tha cube = 6a^2 cm^2

= 6 × (80)^2cm

= 38400 cm^2