3. The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four
walls at the rate of 10 per m² is 15000, find the height of the hall.
(Hint: Area of the four walls =Lateral surface area.]
Answers
Answer:
ANSWER
Given:
Perimeter=250m
⇒Area of 4 walls =2lh+2bh
=2(b+l)h
⇒Perimeter of floor of wall =2l+2b
⇒2(l+b)=250 m
∴ Area of 4 walls =2(l+b)h
=250h m
2
⇒Cost of painting per m
2
area = Rs. 10
⇒Cost of painting 250h m
2
area = Rs(250h×10)
= Rs.2500h
⇒Painting cost of walls = Rs. 15000
⇒2500h=15000
⇒h=
2500
15000
⇒h=6m
Question :-
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹10 per m2 is ₹15000, find the height of the hall.
[Hint: Area of the four walls = Lateral surface area]
Answer :-
A rectangular hall means a cuboid.
Let the length and breadth of the hall be l and b respectively.
∴ Perimeter of the floor = 2(l + b)
⇒ 2(l + b) = 250 m
∵ Area of four walls = Lateral surface area = 2(1 + b) x h, where h is the height of the hall = 250 h m^2
Cost of painting the four walls
= Rs. (10 x 250 h) = Rs. 2500h
⇒ 2500 h = 15000 ⇒ h = 15000/2500 = 6
Thus, the required height of the hall = 6 m
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