Question

Question 7
The lateral surface area of a cube is $256m^2$. The volume of the cube is:

A) $512m^3$
B) $64m^3$
C) $216m^3$
D) $256m^3$​​​​​​​

Answer 1

The answer is A.
Given, lateral surface area of the cube $=256m^2$

We know that, lateral surface area of a cube $=4\times (Side{)}^2$

$\Rightarrow 256=4\times (Side{)}^2$

$\Rightarrow (Side{)}^2=\frac{256}{4}=64$

$\Rightarrow Side=\sqrt{64}=8m$

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

Now, volume of a cube $=(Side{)}^3=(8{)}^3=8\times 8\times 8=512m^3$