Question

If the total surface area of a cuboid whose length is equal to $12\text{cm}$ and breadth is equal to $9\text{cm}$ is equal to $468{\text{cm}}^2$ then find the height of the cuboid.

Answer 1

Total surface area of a cuboid is given by $2(lb+bh+lh)$ where $l$ is length, $b$ is breadth and $h$ is height of the cuboid.

Given:-

$l=12\text{cm}$

$b=9\text{cm}$

$A=468{\text{cm}}^2$

Let the height of the cuboid be $h.$

Then, by using above given formula,

$\begin{array}{cc}468& =2\left(12\times 9+9h+12h\right)\\ 234& =108+21h\\ 21h& =234-108\\ 21h& =126\\ h& =6\text{cm}\end{array}$