Surface Areas & Volumes | Exercise 13.1 | Q3

Question 3: The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs.10 per m² is Rs.15000, find the height of the hall.
[Hint: Area of the four walls = Lateral surface area.]

Video Explanation

Explanatory Answer | Exercise 13.1 Question 3

Given Data

Perimeter of rectangular hall = 2(l + b) = 250 m
Cost of painting 4 walls = Rs.15,000
Cost per m² = Rs.10 per m²

Step 1: Compute Area of Surface Painted

Area of surface painted = \\frac{\text{Total cost of painting}}{\text{Cost per square metre}})
= \\frac{15000}{10})
= 1500 m²

Step 2: Compute Height of Hall

Area covered by 4 walls = Lateral surface area of the room
= 2 (l + b) × h = 1500 m²
The perimeter of the rectangular hall = 2(l + b)
We know 2(l + b) = 250 m
So, area covered by 4 walls = 250 × h = 1500 m²
or h = \\frac{1500}{250}) = 6 m

Height of the hall = 6 m

Exercise 13.1 | Surface Area of Cubes & Cuboids

1. Class 9 Exercise 13.1 Question 3 | Height of hall ▶
2. Class 9 Exercise 13.1 Question 6 | TSA of Herbarium ▶
3. Class 9 Exercise 13.1 Question 7 | Shanti Sweets ▶

Exercise 13.2 | Surface Area of Cylinders

1. Class 9 Exercise 13.2 Question 3 | CSA TSA of Metal Pipe ▶
2. Class 9 Exercise 13.2 Question 4 | Roller & Playground ▶
3. Class 9 Exercise 13.2 Question 9 | Cylindrical Petrol Tank ▶
4. Class 9 Exercise 13.2 Question 10 | CSA of Decorative Lampshade ▶

Exercise 13.3 | Surface Area of Cones

1. Class 9 Exercise 13.3 Question 5 | Length of Tarpaulin 3 m wide ▶
2. Class 9 Exercise 13.3 Question 8 | Cost of painting conical barricades ▶

Exercise 13.4 | Surface Area of Spheres & Hemispheres

1. Class 9 Exercise 13.4 Question 8 | Outer CSA of hemispherical bowl ▶
2. Class 9 Exercise 13.4 Question 9 | Surface area of sphere & Cylinder ▶