Question

The length of cuboid is $12$ cm, breadth and height are equal and its volume is $432{\text{cm}}^3$. The cuboid is cut into $2$ cubes, find the lateral surface area of each cube.

Answer 1

Given, $\ell =12cm$ , Volume $=432c{m}^3$

$b=h$

$\ell \times b\times h=432$

$12\times h^2=432$

$h^2=36$

$h=6$

So $b=6$

Cube should have all sides of same length,
The dimensions of cuboid are $12\times 6\times 6$ and hence it can be cut into two cubes along the side of length $\ell =12cm$

So each cube will have $6\times 6\times 6$ dimensions.

Hence, side of cube $a=6$

Lateral surface area of cube $=4a^2$

$=4\times 6^2$

$=144c{m}^2$