Total Surface Area of Cylinder | Exercise 13.2 | Q3

Question 3: A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. (As shown in the adjacent figure). Find its
(i)  Inner curved surface area
(ii)  Outer curved surface area
(iii)  Total surface area

Video Explanation

Explanatory Answer | Exercise 13.2 Question 3

Given Data:
Height of the cylindrical pipe is 77 cm.
Inner diameter = 4 cm. So, inner radius = 2 cm.
Outer diameter = 4.4 cm. So, outer radius = 2.2 cm.

Part (i): Inner Curved Surface Area of Cylinder

Curved Surface Area of Cylinder = 2 × π × r × h
Because we are computing inner curved surface area, the radius to be used is the inner radius.
Inner radius of the cylindrical metal pipe = 2 cm

Take π = \\frac{22}{7})
Inner Curved Surface Area (CSA) of Cylinder = 2 × \\frac{22}{7}) × 2 × 77 = 44 × 22
Inner CSA = 968 cm²

Part (ii): Outer Curved Surface Area of Cylinder

Curved Surface Area of Cylinder 2 × π × r × h
Because we are computing outer curved surface area, the radius to be used is the outer radius.
Outer radius = 2.2 cm

Take π = \\frac{22}{7})
Outer Curved Surface Area (CSA) of cylinder = 2 × \\frac{22}{7}) × 2.2 × 77 = 44 × 24.2
Outer CSA = 1064.8 cm²

Part (iii): Total Surface Area of Cylinder

What does it include?
1. The inner curved surface area
2. The outer curved surface area
3. The area of the circular ring on the top and the bottom surface of the metal pipe

We have computed inner and outer surface areas. So, we have to calculate only the area of the circular ring.

Area of the circular ring = area of outer circle - area of inner circle
Area of circular ring = πr_o² - πr_i² where r_o is the outer radius and r_i is the inner radius.

Area of one circular ring = π(r_o² - r_i² ) = π(r_o + r_i)(r_o - r_i)
= \\frac{22}{7}) (2.2 + 2) (2.2 - 2)
= \\frac{22}{7}) × 4.2 × 0.2
= 2.64 cm²

Area of the circular rings at the top and the bottom: We have to count the area of the circular rings at the top and the bottom.
So, area of both the circular rings = 2.64 × 2 = 5.28 cm²

Total Surface Area of Cylinder = 968 + 1064.8 + 5.28 = 2038.08 cm²

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 ▶