Question

If the volume of a square-based prism is $250c{m}^2$ and height is $10$cm, find the total surface area.

Answer 1

The general formula for volume of prism is $V=s^{2}h$ where $s$ is the base and $h$ is the height.

Since volume of the prism is $V=250$ cm${}^2$ and the height $h=10$ cm, therefore, the area of base is:

$V=s^{2}h\Rightarrow 250=10s^2\Rightarrow s^2=\frac{250}{10}=25\Rightarrow s=\sqrt{25}=5$

Now, the perimeter $P$ of the prism is $P=4\times side$, therefore, the perimeter of prism with side $5$ cm is $P=4\times 5=20$ cm.

The general formula for the total surface area of a right prism is $TSA=Ph+2B$ where $P$ represents the perimeter of the base, $h$ is the height of the prism and $s$ is the base.

$TSA=Ph+2s^2=(20\times 10)+(2\times 25)=200+50=250$ cm${}^2$

Hence, the total surface area is $250$cm${}^2$.