**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

**Solution:**

(a) 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.