Question

A room is 8m long, 4.5 wide and 2.8m high. It has one door 1.4m wide and 2 metre high with a semicircular ventilator as shown in figure and two rectangular Windows 2m by 1.5m each. Find the cost of whitewashing the inner walls of the room at the rate of 10 rupees per metre square (take pie equal to 22 by 7 )

Answer 1

According to question for room.

L = 8m
B = 4.5m
H = 2.8m

So the total area of the walls of room  

A = 2(L+B)H
A = 2(4+8.5)2.8
 A = 70 m^2

According to question.

Area of Door 
                       a1 = 1.4*2+ pi/2* 0.7^2
                       a1 = 3.57 m^2
area of 2 windows
                      a2 = 2*2 * 1.5
                       a2 = 6 m^2
Now are to be white washed = A-(a1+a2)
 Thus               A' = 70-(3.57+6)
                        A' = 70 - 9.57
                        A' = 60.43 m^2
For 1 m^2 cost of white wash  = 10 rupees
Now cost for 60.43 m^2 = 60.43*10
                                        =  604.3 Rupees
              

Answer 2

Solution :-

Length of the room = 8 m
Width of the room = 4.5 m
Height of the room = 2.8 m

Area of the four walls of the room = 2H(L + B)

⇒ 2*2.8*(8 + 4.5)

⇒ 5.6*12.5

= 70 m²

Length of the door = 2 m
Breadth of the door = 1.4 m

Area of the door = L*B

⇒ 2*1.4

= 2.8 m²

Diameter of the semicircular ventilator = 1.4 m

Radius = 1.4/2 

= 0.7 m

Area of the semicircular ventilator = (πr²)/2

⇒ 22/7*0.7*0.7*1/2

⇒ 0.77 m²

Length of 1 rectangular window = 2 m
Breadth of 1 rectangular window = 1.5 m

Area of 1 rectangular window = 2*1.5

= 3 m²

Area of 2 rectangular windows = 3*2

= 6 m²

Area of the region to be whitewashed = Area of 4 walls - (Area of the door + Area of the Semicircular Ventilator + Area of 2 Rectangular Windows)

⇒ 70 - (2.8 + 0.77 + 6)

⇒ 70 - 9.57

⇒ 60.43 m²

Rate of whitewashing = 10 sq m

Total cost of whitewashing = 60.43*10 

= Rs. 604.3

Answer.