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Question

The dimensions of a room are $$14m \times  10 m \times  6.5 m$$. There are two doors and 4 windows in the room. Each door measures $$2.5\,m \times  1.2\,m$$ and each window measures $$1.5 \times  1 m$$. Find the cost of painting the four walls of the room at RS 35 per $$m^2$$.


Solution

Dimensions of wall:
Length = 14 m
Breadth = 10 m
Height = 6.5 m
Dimensions of windows
Length = 1.5 m
Breadth = 1 m
And,Length of doors = 2.5 m
Breadth of doors = 1.2 m
Cost = RS 35 per $$m^2$$
Now,
Area of four walls $$=$$ 2(Length of walls $$\times$$  Height of walls) $$+ 2$$(Breadth of walls $$\times $$ Height of walls)
$$= 2(14 \times  6.5) + 2(10 \times  6.5)$$
$$= 182 + 130$$
$$= 312$$
$$\Rightarrow $$ Area of four walls is $$312\,m^2$$
Area of two doors $$=$$ 2(Length of doors $$\times $$ Breadth of doors)
$$= 2(2.5 \times  1.2)$$
$$= 6$$
$$\Rightarrow $$ Area of two doors is $$6\,m^2$$
Area of four windows $$=$$ 4(Length of windows $$\times $$ Breadth of windows)
$$= 4(1.5 \times  1)$$
$$= 6$$
$$\Rightarrow $$ Area of four windows is $$6\,m^2$$
Therefore,
Area to be painted $$=$$ Area of 4 walls $$-$$ (Area of 2 doors $$+$$ Area of 4 windows)
$$= 312 (6+ 6)$$
$$= 300$$
$$\Rightarrow $$ Area to be painted is $$300\,m^2$$
Cost of painting $$= 300 m^2 \times $$ Rs 35 per $$m^2$$
$$ = Rs\,10500 $$

Mathematics
RS Agarwal
Standard IX

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