Question

The length, breadth and height of a room are $5m$, $4m$ and $3m$ respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of $Rs7.50per{m}^2$

Answer 1

Dimensions of the room are,

lentgth $\left(l\right)=5m$

breadth $\left(b\right)=4m$

height $\left(h\right)=3m$

$S=$ The total surface area to whitewash

$A_1=$ The lateral surface area of the room

$A_2=$ The surface area of the ceiling

$R=$The rate of whitewashing per $m^2$

We know that,

$R=Rs7.50m^2$

We are asked to find the cost of whitewashing

Now, the total surface area to whitewash,

$S=A_1+A_2$ [ lateral surface area = Area of four wall $=2(l+b)h]$

$=\left[2\right(l+b)h+lb]$ [Surface area of ceiling $=l\times b$]

$=\left[2\right(5+4)\times 3+5\times 4]$

$=74m^2$

The total cost of whitewashing,

$=S\times R$

$=\left(74m^2\right)\times \left(Rs7.50per{m}^2\right)$

$=Rs555$

Hence the cost of whitewashing the room and the ceiling is $Rs555$.