Question

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

Answer 1

Calculate the cost of whitewashing:

The length $\left(l\right)$, breadth $\left(b\right)$, and height$\left(h\right)$ of a room are $5\mathrm{m},4\mathrm{m}\mathrm{and}3\mathrm{m}$respectively.

The diagram is shown below,

The orange color top surface is the ceiling and remaining the four vertical surfaces are walls of the room.

Area of whitewashing $=$ area of walls $+$ area of the ceiling

$\begin{array}{rcl}& =& 2lh+2bh+lb\\ & =& \left(2\times 5\times 3\right)+\left(2\times 4\times 3\right)+\left(5\times 4\right)\\ & =& 30+24+20\\ & =& 74{\mathrm{m}}^2\end{array}$

Since, the rate of whitewashing is $\mathrm{Rs}.7.50\mathrm{per}{\mathrm{m}}^2$.

Thus, the total cost of whitewashing$=74\times 7.50=\mathrm{Rs}.555$

Hence, the total cost of whitewashing is $\mathrm{Rs}.555$.