# Ex.13.1 Q3 Surface Areas and Volumes - NCERT Maths Class 9

## Question

The floor of a rectangular hall has a perimeter \(250\,\rm{ m}\). If the cost of painting the four walls at the rate of \(\begin{align}\text{Rs. 10 per }\rm{m^2} \end{align}\) is \(\rm{Rs}. 15000,\) find the height of the hall.

[**Hint:** Area of the four walls = Lateral surface area.]

## Text Solution

**What is the known?**

Perimeter of the hall which is

\(\begin{align}2(l + b) = 250\,\rm{m}\end{align}\) and the cost of painting at the rate of \(\begin{align} \text{Rs.10 per}\,\rm {m^2} \end{align}\) is \(\rm{Rs}. 15000.\)

**What is the unknown?**

Height of the hall.

**Reasoning:**

Lateral surface area of the cuboid is only the area of \(4\) walls of the cuboid. Lateral surface area of cuboid \(\begin{align} = 2(l + b)h \end{align}\). So, the ratio between the total cost for painting and cost per \(\rm{m^2}\) will give the total lateral surface area painted.

**Steps:**

The ratio between the total cost for painting and cost per \(\rm{m^2}\) will give the total lateral surface area painted.

Area of four walls

\[\begin{align}&=\frac{{15000}}{{10}}\\&= 1500 \end{align}\]

Perimeter \(= [2\,\,(l + b)] = 250\,\rm{m}\)

\[\begin{align}2(l + b)h &= 1500 \\(250 \times h) &= 1500\\h &= \frac{{1500}}{{250}}\\&= 6\,\rm{m} \end{align}\]

The height of the hall is \(6\,\rm {m.}\)