Question

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

Answer 1

Length of a door = 2.5 m

Breadth of the door = 1.2 m

area of the door = l $\times$ b = 2.5 m $\times$ 1.2 m = 3 $m^2$

∴ area of 2 doors = 2 $\times$ 3 = 6 $m^2$ ​​​​​​​

Length of the window = 1.5 m

Breadth of the window = 1 m

Area of the window = l $\times$ b = 1.5$\times$ 1 = 1.5 $m^2$ ​​​​​​​

∴ area of 4 windows = 4 $\times$ 1.5 = 6 $m^2$ ​​​​​​​

Area of the doors + Area of the windows = 6 $m^2$ ​​​​​​​ + 6 $m^2$ ​​​​​​​ = 12 $m^2$ ​​​​​​​

Length of the wall = 12.5 m

Breadth of the wall = 9 m

Height of the wall = 7 m

Area of the wall = LSA of a cuboid = 2h(l+b)

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

= 14 $\times$ 21.5 = 301 $m^2$ ​​​​​​​

Required area of the wall to be painted = Area of the wall - Area of the doors and windows

i.e., area of the wall to be painted = 301 m2 - 12 $m^2$ ​​​​​​​

area of the wall to be painted = 289 $m^2$ ​​​​​​​

Cost of painting 1 $m^2$ ​​​​​​​ of the wall = Rs. 3.50

Cost of painting 289 $m^2$ ​​​​​​​ of the wall = Rs. (3.50 $\times$ 289)

Cost of painting the wall = Rs. 1011.5