Question

Find the area of four walls of a room having length, breadth, and height as 8 m, 5 m, and 3 m respectively. Find the cost of white-washing the walls at the rate of Rs. $15/{{m}^{2}}.$

Answer 1

Hint: Find the area of four walls using the formula \[\text{Area of four walls} =2\times \left( \text{length+breadth} \right)\times \text{height}''\]
In the question, the cost of whitewash per meter is given, multiply this rate with the above-calculated area to get the cost of whitewashing the wall’s total.

Complete step-by-step solution:
We have given;
The length of the room = l = 8 m
The breadth of the room = b = 5 m
The height of the room = h = 3 m

We have the formula to find the area of four walls.
\[\text{Area of four walls} = 2\times \left( \text{length+breadth} \right)\times \text{height}''\]
Putting the values of length, breadth and height in the formula, we get;
$\text{Area of four walls}=\left\{ 2\left( 8+5 \right) \right\}\times 3$
$\begin{align}
  & =2\times 13\times 3 \\
 & =78{{m}^{2}}...................\left( 1 \right) \\
\end{align}$
Given, the rate of whitewashing $=Rs.\ 15/{{m}^{2}}.$
Hence, total cost of whitewashing the walls \[=\left( \text{Area of four walls} \right)\times \text{Rate of white washing}\]
\[\begin{align}
  & =\left( 78{{m}^{2}} \right)\times Rs.\ 15\ per\ {{m}^{2}} \\
 & =Rs.\ 1170 \\
\end{align}\]

Note: Students can do mistakes in this question by adding the area of ceiling to the area of four walls to get the total area of whitewashing. But in the question, it has to calculate the total cost of whitewashing the walls. So, we will not add an area of the ceiling for whitewashing here.