Question

A laboratory is 9m long, 8m wide and 6m high. It has 2 doors each of size $3m \times 1.5m$ and 4 windows each of size $1.5m \times 1m$ . Find the cost of whitewashing the walls of the laboratory at the rate of Rs. 1.75 per square meter.

Answer 1

Hint- For such type of questions we just have to keep in mind that we have to exclude the area occupied by the windows and doors from the total area because we are not going to whitewash on that area and thus we have to calculate the cost on the basis of cost of white washing as given per square meter. Also, we have to calculate the lateral surface area of the laboratory here because we are only going to whitewash the walls and not the floor and the ceiling.

Complete step-by-step answer:

Length of the laboratory $(l) = 9m$
Width of the laboratory $(b) = 8m$
Height of the Laboratory $(h) = 6m$

Since, we know that the laboratory must be of the shape of a cuboid so we have to calculate the lateral surface area of the cuboid or we can say that we have to calculate the area of the four walls except the ceiling and the floor.
$\therefore $ Area of the Four walls of the Laboratory $ = 2 \times (l + b) \times h = 2 \times (9m + 8m) \times 6m$
                                                                              $ = 2 \times 17m \times 6m = 204{m^2}$
Now, we have to remove the area occupied by the 2 doors and the 4 windows
First consider the doors, Length of a door $(l) = 3m$ and width of a door $(b) = 1.5m$
Area of a door $ = l \times b = 3m \times 1.5m = 4.5{m^2}$ (as door is a type of rectangle)
Area of 2 doors $ = 2 \times 4.5{m^2} = 9{m^2}$
Now we will consider the windows, Length of a window $(l) = 1.5m$ and width of a window $(b) = 1m$
Area of a window $ = l \times b = 1.5m \times 1m = 1.5{m^2}$ (as window is also a type of rectangle)
Area of 4 windows $ = 4 \times 1.5{m^2} = 6{m^2}$
Now, area to be whitewashed = Area of 4 walls – Area of two doors – Area of 4 windows
                                                       $ = 204{m^2} - 9{m^2} - 6{m^2} = 189{m^2}$
Now since we have the area to be white washed so we have to find the cost now.
Cost of white washing per square meter $ = Rs.1.75$
Cost of white washing $189{m^2} = Rs.1.75 \times 189 = Rs.330.75$
Hence, the required cost to white wash the walls of the laboratory at the cost of Rs.1.75 per square meter is $Rs.330.75$

Note- Just remember in such type of questions we have to calculate the area of the four walls of the cuboid which is $ = 2(l + b)h$ where $l = $ length of the cuboid, $b = $ width of the cuboid and $h = $ height of the cuboid.