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

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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.]

 Video Solution
Surface Areas And Volumes
Ex 13.1 | Question 3

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 \(6\,\rm {m.}\)

  
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