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The dimensions of a metallic cuboid a...

The dimensions of a metallic cuboid are: `100\ c mxx80xx64\ c m` . It is melted and recast into a cube. Find the surface area of the cube.

A

`58400 cm^2`

B

`38400 cm^2`

C

`39400 cm^2`

D

`36400 cm^2`

Text Solution

Verified by Experts

The correct Answer is:
B
Let each of the cube be a.
Then, volume of the cube `=a^3`
Volume of the cube `=(100xx 80 xx 64 ) cm ^3`
`=512000 cm^3`
Volume of the cube = volume of the cuboid
`rArr a^3 = 512000 cm^3`
`rArr a=root(3)(512 xx 1000 ) cm = (8xx10)cm=80cm `
Surface area of the cube `= 6a^2`
`= (6xx 80 xx 80 ) cm^2 = 38400 cm^2`
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