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 mBreadth = 10 mHeight = 6.5 mDimensions of windowsLength = 1.5 mBreadth = 1 mAnd,Length of doors = 2.5 mBreadth of doors = 1.2 mCost = 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 $$m^2$$$$= Rs\,10500$$MathematicsRS AgarwalStandard IX

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