Question

The lateral surface area of a cube is 256 m². The volume of the cube is 

A. 512 m³  

B. 64 m³ 

C. 216 m³ 

D. 256 m³

Answer 1

(A) 512 m³

Given, lateral surface area of a cube = 256 m²
We know that, lateral surface area of a cube = 4 x (Side)²

=> 256 = 4 x (Side)²

=> (Side)² = 256/4 = 64

=> Side = √64 = 8 m

[taking positive square root because side is always a positive quantity]

Now, volume of a cube = (Side)³ 

= (8)³ 

= 8 x 8 x 8 

= 512 m³

Hence, the volume of the cube is 512 m³.