Question

A hall is $15m$ long and $12m$ broad, the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls.

Find the volume of the hall?

Answer 1

Step-1: Solve for height of hall

Given: $length\left(l\right)=15m,breadth\left(b\right)=12m$

Let the height be $h$

According to the equation

sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls

area of floor$=l\times b$

area of ceiling$=l\times b$

area of wall$=2(l+b)h$

so, the equation will become

$$\begin{gathered} l\times b+l\times b=2\left(l+b\right)\times h \\ \Rightarrow lb=lh+bh \\ \Rightarrow 15\left(12\right)=15\left(h\right)+12\left(h\right) \\ \Rightarrow 180=27h \\ \Rightarrow h=\frac{20}{3} \end{gathered}$$

Step-2: Solve for the volume of the height

Volume of hall$=l\times b\times h$

$$\begin{gathered} =15\times 12\times \frac{20}{3} \\ =1200 \end{gathered}$$

Hence, the volume of hall$=1200m^3$.