Surface Areas & Volumes | Exercise 13.2 | Q9

Question 9: Find

(i) the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high
(ii) how much steel was actually used if \\frac{1}{12}) of the steel actually used was wasted in making the tank.

Video Explanation

Explanatory Answer | Exercise 13.2 Question 9

Part (i) Lateral surface area of a right circular cylinder

Lateral surface area of a right circular cylinder = 2πrh
Take π = \\frac{22}{7})

Height of the cylindrical tank is 4.5 m
Diameter of the tank = 4.2 m
So, the radius of the tank = 2.1 m = \\frac{21}{10}) m

Curved surface area of cylinder or lateral surface area of cylinder = 2 × \\frac{22}{7}) × \\frac{21}{10}) × 4.5
= \\frac{22 × 27}{10}) = 59.4 m²

Part (ii): Area of steel required to make closed storage tank

It is a closed storage tank. So, area of steel used to make the tank is the total surface area of the cylinder.
Total surface area of cylinder = curved surface area of cylinder + 2 × area of circular base (one for the top and the other for the base).
We have already computed the curved surface area to be 59.4 m²

To compute the TSA, let us add the areas of the two circles, one at the top and the the other at the bottom.
Area of each circle = πr² = \\frac{22}{7}) × \\frac{21}{10}) × \\frac{21}{10}) = \\frac{22 × 3 × 21}{100}) = 13.86 m²

Total surface area of cylinder = curved surface area + (2 × Area of one circle)
= 59.4 + (2 × 13.86)
Total surface area = 87.12 m²

Steel used to make the tank

\\frac{1}{12})th of steel used was wasted in making the tank.
So, 1-\\frac{1}{12}) = \\frac{11}{12})th of the steel was used to make the tank.

\\frac{11}{12}) of the steel used = 87.12 m²
∴ Total steel used = 87.12 × \\frac{12}{11}) = 95.04 m²

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 ▶