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.]
Solution:
Given: The perimeter of the floor of the rectangular hall is 250m and the cost of painting the four walls at the rate of ₹10 per m² is ₹15000.
The area of the four walls of the cuboidal room will be the Lateral surface area of the cuboid.
Lateral surface area of cuboid = 2(l + b)h
The area of the four walls can also be obtained by dividing the total cost of the painting by the rate of painting per m2.
Let the length, breadth, and height of the room be l, b, and h respectively. The cost of painting the four walls is ₹15000.
The rate of painting is ₹10 / m2
Perimeter of the floor = 250 m
Therefore, 2(l + b) = 250 m ------------ (1) [Since, perimeter of a rectangle = 2(l + b)
Now, Area of four walls = 15000/10 m2 = 1500 m2
2(l + b)h = 1500 m2 [From equation(1)]
250 m × h = 1500 m2
h = 1500 m2/250 m = 6 m
Thus, the height of the hall is 6 m.
☛ Check: NCERT Solutions Class 9 Maths Chapter 13
Video Solution:
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.]
Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.1 Question 3
Summary:
It is given that the floor of a rectangular hall has a perimeter 250 m and the cost of painting the four walls at the rate of ₹10 per m2 is ₹15000. We have found that the height of the hall is 6 m.
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