Question

The length, breadth and height of a room are $5m,4m$ and $3m$ respectively. Find the cost of washing the walls of the room and ceiling at the rate of Rs. $7.50$\[per{\text{ }}{m^2}\].

Answer 1

Hint: Here, we have calculate the area to be whitewashed, so it does not include the area of floor and can be calculated by using the following formula:
Area to be whitewashed = Area of four walls + Area of Ceiling

Complete step-by-step answer:
Given-
Length of the room, $l = 5m$
Breadth of the room, $b = 4m$
Height of the room, $h = 3m$
Area to be whitewashed does not include the floor.
Therefore, Area to be whitewashed = Area of four walls + Area of Ceiling
$\therefore $ Area to be whitewashed = $2h\left( {l + b} \right) + lb$
\[ \Rightarrow \] Area to be whitewashed = $2 \times 3\left( {5 + 4} \right) + 5 \times 4$
\[ \Rightarrow \] Area to be whitewashed = $6 \times 9 + 20$
\[ \Rightarrow \] Area to be whitewashed = $54 + 20$
\[ \Rightarrow \] Area to be whitewashed = $74{m^2}$
Cost of white washing of $1{m^2} = Rs.7.50$
$\therefore $Total cost of white washing= $Rs.7.50 \times 74$
\[ \Rightarrow \]Total cost of white washing= $Rs.555$

The total cost for white washing is Rs.555

Note: The area to be white washed can also be calculated as follows:
Area to be whitewashed = Area of cuboid – Area of Base
$\therefore $ Area to be whitewashed = $2\left( {lb + bh + hl} \right) - lb$
\[ \Rightarrow \] Area to be whitewashed = $2\left( {5 \times 4 + 4 \times 3 + 3 \times 5} \right) - 5 \times 4$
\[ \Rightarrow \] Area to be whitewashed = $2\left( {20 + 12 + 15} \right) - 20$
\[ \Rightarrow \] Area to be whitewashed = $2\left( {47} \right) - 20$
\[ \Rightarrow \] Area to be whitewashed = $94 - 20$
\[ \Rightarrow \] Area to be whitewashed = $74{m^2}$