Two cubes, each of volume $512\ cm^3$ are joined end to end. Find the surface area of the resulting cuboid.

Given:

Two cubes, each of volume $512\ cm^3$ are joined end to end.

To do:

We have to find the surface area of the resulting cuboid.

Solution:

Volume of each cube $= 512\ cm^3$

This implies,

Edge of the cube $= \sqrt[3]{512}$

$=8\ cm$

The length of the cuboid formed by joining the cubes $(l) = 8 + 8$

$= 16\ cm$

Breadth of the cuboid $(b) = 8\ cm$

Height of the cuboid $(h) = 8\ cm$

Therefore,

Surface area of the resulting cuboid $= 2(lb + bh + lh)$

$= 2(16 \times 8 + 8 \times 8 + 8 \times 16)$

$= 2(128 + 64 + 128)$

$= 2 \times 320$

$= 640\ cm^2$