Question

The length of cold storage is twice its breadth. The height is $3$ meters and the area of its four walls (including doors) is $108{\mathrm{m}}^2$. Find its volume?

Answer 1

Calculate the volume :

Let the length, breadth, and height of the cold storage be $l,b\mathrm{and}h$respectively.

Given that, $l=2b,h=3\mathrm{m}$

Since the area of its four walls (including doors) is $108{\mathrm{m}}^2$.

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{four}\mathrm{walls}=108m^2 \\ \Rightarrow 2lh+2bh=108 \\ \Rightarrow h(l+b)=54 \\ \Rightarrow 3(2b+b)=54\left[\because l=2b,h=3\mathrm{m}\right] \\ \Rightarrow 9b=54 \\ \Rightarrow b=\frac{54}{9} \\ \Rightarrow b=6\mathrm{m} \end{gathered}$$

So, $l=2\times 6=12\mathrm{m}$

Thus, the length, breadth, and height of the cold storage are $12\mathrm{m},6\mathrm{m}\mathrm{and}3\mathrm{m}$ respectively.

$\begin{array}{rcl}\mathrm{Volume}& =& l\times b\times h\\ & \Rightarrow & =12\times 6\times 3\\ & \Rightarrow & =216{\mathrm{m}}^3\end{array}$

Hence, the volume of the cold storage is $216{\mathrm{m}}^3$.