 # The dimensions of a room are 12.5 m by 9 m by 7 m.

Question:

The dimensions of a room are 12.5 m by 9 m by 7 m. There are 2 doors and 4 windows in the room; each door measures 2.5 m by 1.2 m and each window 1.5 m by 1 m. Find the cost of painting the walls at Rs 3.50 per square metre.

Solution:

The dimensions of the room are $12.5 \mathrm{~m} \times 9 \mathrm{~m} \times 7 \mathrm{~m}$.

Hence, the surface area of walls $=2 \times($ length $\times$ height $+$ breadth $\times$ height $)$

$=2 \times(12.5 \times 7+9 \times 7)$

$=301 \mathrm{~m}^{2}$

Also, there are 2 doors and 4 windows in the room.

The dimensions of door are $2.5 \mathrm{~m} \times 1.2 \mathrm{~m} .$

i. e., area of a door $=2.5 \times 1.2=3 \mathrm{~m}^{2}$

$\therefore$ Total area of 2 doors $=2 \times 3=6 \mathrm{~m}^{2}$

The dimensions of a window are $1.5 \mathrm{~m} \times 1 \mathrm{~m} .$

i. e., area of a window $=1.5 \times 1=1.5 \mathrm{~m}^{2}$

$\therefore$ Total area of 4 windows $=4 \times 1.5=6 \mathrm{~m}^{2}$

Hence, the total area to be painted $=301-(6+6)=289 \mathrm{~m}^{2}$

The rate of painting $1 \mathrm{~m}^{2}$ of wall $=\mathrm{Rs} 3.50$

$\therefore$ The total cost of painting $289 \mathrm{~m}^{2}$ of wall $=\mathrm{Rs} 289 \times 3.50=\mathrm{Rs} 1011.50$