# NCERT Solutions For Class 9 Math | Exercise 13.2

###### Chapter: Surface Areas & Volumes | Curved & Total Surface Area of Cylinder

Exercise 13.2 of class 9 NCERT math text books comprises 11 questions. This exercise focuses on curved surface area and total surface area of right circular cylinders. Video solutions to questions 3, 4, 9, and 10 are provided below. Detailed explanation to all 11 questions are provided below.

#### What is formula of curved surface area of cylinder? How to find the curved surface area of a cylinder?

The formula to compute the curved surface area of cylinder is 2πrh, where 'r' is the radius of the base of the right circular cylinder and 'h' is the height of the cylinder.

The curved surface area of cylinder is the product of the circumference and the height.

#### What is the formula of total surface area of cylinder? How to find the surface area of a cylinder?

The formula to compute the total surface area of cylinder is 2πr(r + h), where 'r' is the base radius of the right circular cylinder and 'h' is the height of the right circular cylinder.

The total surface area of cylinder, TSA, is the sum of the curved surface area of the cylinder and the area of the two circles - one at the top and the other at the bottom of the cylinder.
TSA of cylinder = 2πrh + 2πr2 = 2πr(r + h)

1. Question 1

The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder.

2. Question 2

It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?

3. 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

4. Question 4

The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2.

5. Question 5

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs.12.50 per m2.

6. Question 6

Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find its height.

7. Question 7

The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find
(i) Its inner curved surface area
(ii) The cost of plastering this curved surface at the rate of Rs.40 per m2

8. Question 8

In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.

9. 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 [1/12] of the steel actually used was wasted in making the tank.

10. Question 10

In the adjacent figure (figure 13.12 in class 9 NCERT book page 217), you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade

11. Question 11

The students of a Vidyalaya were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

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