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The lateral surface area of a cube us 2...

The lateral surface area of a cube us `256m^(2)`. The volume of the cube is.

A

`512m^(3)`

B

`64m^(3)`

C

` 216 m^(3)`

D

`256 m^(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given,lateral surface area of a cube = `256 cm^(2)`
We know that, lateral surface area for a cube `= 4 xx ("Side")^(2)`
`rArr " "256 = 4xx ("side")^(2)`
`rArr " "("Side")^(2) =(256)/(4) = 64`
`rArr " "("Side") = sqrt(64) = 8 m`
[ taking positive square root because side is always a positive quantity ]
Now, Volume of a cube ` = ("side")^(3) = (8)^(3) = 8 xx 8xx 8 = 512m^(3)`
Hence, the volume of the cube is `512m^(3)`.
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