Surface Areas & Volumes | Exercise 13.3 | Q5

Question 5: What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume the extra length of the material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π = 3.14).

Video Explanation

Explanatory Answer | Exericse 13.3 Question 5

Given Data:
Height of the conical tent, h = 8 m
Radius of the conical tent, r = 6 m
Width of the tarpaulin sheet, b = 3 m
Length of the extra tarpaulin material used = 20 cm = \\frac{20}{10}) m = 0.2 m

Step 1: Compute Slant Height of Cone

Square of slant height of the conical tent, l²= r² + h²
l² = 6² + 8²
l² = 36 + 64 = 100
∴ slant height of cone, l = 10 m

Step 2: Compute Curved Surface Area of Cone

Curved surface area of the conical tent = π × r × l
Take π = 3.14
= 3.14 × 6 × 10
= 188.4 m²

Step 3: Compute Area of Tarpaulin Sheet Required

Area of the tarpaulin sheet = Curved surface area of the conical tent
It is a rectangular sheet. Let its length be L m and breadth be B m.
L × B = 188.4
L × 3 = 188.4
L = 62.8 m
Length of the tarpaulin sheet required = Length computed above + Length of the extra tarpaulin material used for stitching margin and wastage
= 62.8 + 0.2
Length of the tarpaulin sheet = 63 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 ▶