Question

# The lateral surface area of cube is $256{m}^{2}$. Find its volume.

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Solution

## Step 1: Find the edge of the cube.The lateral surface area of cube $=256{m}^{2}$Let us consider $a$ as the edge of the cube.The lateral surface area of a cube $=4{a}^{2}$$⇒256=4{a}^{2}\phantom{\rule{0ex}{0ex}}⇒{a}^{2}=256/4\phantom{\rule{0ex}{0ex}}⇒{a}^{2}=64\phantom{\rule{0ex}{0ex}}⇒a=8m$Step 2: Find the volume of the cube.The volume of the cube $={a}^{3}={8}^{3}=512{m}^{3}$Hence, The volume of the cube is $512{m}^{3}$.

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