The length, breadth, and height of a room are $5m$, $4m$ and $3m$ respectively. Find the cost of white washing the walls of the rooms and the ceiling at the rate of $Rs.7.50$ per $m^2$.

The correct option is D: $Rs.555$

Dimension of the room is : $5m\times 4m\times 3m$

Surface area of $4$ walls $=2h(l+b)$

and, surface area of ceiling $=l\times b$

Total surface area to be painted is

$=$ Surface area of walls $+$ ceiling area

$=\left[2h\right(l+b\left)\right]+(l\times b)$

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

$=(2\times 3\times 9)+20$

$=54+20$

$=74m^2$

Cost of white washing $1m^2$ area $=Rs.7.50$

Therefore, the cost of white the $4$ walls and ceiling $=Rs.(74\times 7.50)=Rs.555$