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

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

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Solution

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

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

$\Rightarrow 256 = 4 \times (S i d e)^{2}$

$\Rightarrow (S i d e)^{2} = \frac{256}{4} = 64$

$\Rightarrow S i d e = \sqrt{64} = 8 m$

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

Now, volume of a cube $= (S i d e)^{3} = (8)^{3} = 8 \times 8 \times 8 = 512 m^{3}$

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

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

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

256

^{2}

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