## NCERT Class 10 Maths Lab Manual – Surface Area of a Cylinder

**Objective**

To find the curved surface area and total surface area of a cylinder experimentally.

**Prerequisite Knowledge**

- Area of a rectangle.
- Area of a circle.
- Concept of surface area of a cylinder.

You can also download **NCERT Maths Class 10 Solutions** to help you to revise complete syllabus and score more marks in your examinations.

**Materials Required**

A white chart paper, a cylinder made of paper, a pair of scissors, a ruler, fevicol.

**Procedure**

- Remove the top and bottom circles of the cylinder.
- Make a vertical cut in the curved surface and lay the cylinder flat to get a rectangle as shown.
- Measure the length and breadth of the rectangle so formed.

**Observation**

- Top and bottom of cylinders are circles.

Therefore Area of 2 circles = \(\pi { r }^{ 2 }\), where r is the radius of base circle of cylinder - Length of rectangle = circumference of base of cylinder = \(2\pi \)r
- Breadth of rectangle = height = h
- Area of rectangle = \(\pi { r }\)x h = curved surface area of cylinder
- Total surface area of cylinder =\(2\Pi rh\) + \(\pi { r }^{ 2 }\)

= \(2\Pi r(h+r)\)

**Result**

Curved surface area of a cylinder = \(2\Pi rh\)

Total surface area of a cylinder = \(2\Pi r\) (h+r)

**Learning Outcome**

This activity’ clears the concept of curved surface area (lateral surface area) and total surface area of a cylinder.

**Activity Time**

Calculate the total surface area in terms of radius, where ‘tf represents the diameter of the cylinder.

**Viva voice**

**Question 1:**

What is curved surface area of a cylinder ?

**Answer:**

\(2\Pi rh\)

**Question 2:**

What is total surface area of a cylinder ?

**Answer:**

\(2\Pi r(r+h)\)

**Question 3:**

Write the number of circular faces of a cylinder ?

**Answer:**

2

**Question 4:**

What is the area of a circular face of cylinder ?

**Answer:
** \(\pi { r }^{ 2 }\)

**Question 5:**

If h = 7 cm and r=2 cm, find the lateral surface area of a cylinder.

**Answer:
**\(2\Pi rh\)=2× \(\frac { 22 }{ 7 } \) ×2×7= 88 cm

^{3}

**Question 6:**

What is the total area of circular faces of a cylinder ?

**Answer:**

\(2{\pi }{r}^{2}\)

**Question 7:**

What will be the curved surface area of a cylinder if its height is 3 times of its radius ?

**Answer:**

\(6{\pi }{ r }^{ 2}\)

**Question 8:**

What will be the curved surface area of a cylinder if its height is equal to the diameter of the base ? **Answer:**

\(4{\pi }{ r }^{2}\)

**Multiple Choice Questions**

**Question 1:**

The curved surface area of a right circular cylinder of height 14 cm is 88 cm^{2}. The diameter of the base of

the cylinder is

(a) 2 cm

(b) 1 cm

(c) 1.5 cm

(d) none of these

**Question 2:**

The curved surface area of a right circular cylinder is 4.4 m^{2} . If the radius of the base of the cylinder is

0.7 m, find its height.

(a) 2 m

(b) 1.5 m

(c) 1 m

(d) none of these

**Question 3:**

A cylindrical pillar is 5 m 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 m^{2}

(d) Rs. 69.75

(b) Rs. 687.5

(c) Rs.67.75

(d) none of these

**Question 4:**

A rectangular sheet of paper 44 cm x 18 cm is rolled along its length and a cylinder is formed. The radius of the cylinder is

(a) 7 cm

(b) 9 cm

(c) 22 cm

(d) none of these

**Question 5:**

The radius and height of a cylinder are in the ratio 5 : 7 and its curved surface area is 220 cm^{2}. The radius and height are respectively

(a) 5 cm and 7 cm

(b) 7 cm and 5 cm

(c) 5 cm and 5 cm

(d) 1 cm and 7 cm

**Question 6:**

The curved surface area of a cylinder is 1000 cm^{2 }and its diameter is 20 cm. The height of the cylinder is

(a) 15.9 cm

(b) 15.8 cm

(c) 19.5 cm

(d) none of these

**Question 7:**

Find the curved surface area of a right circular cylinder of height 14 cm and base radius 1 cm.

(a) 88 cm^{2
}(b) 80 cm^{2
}(c) 82 cm^{2
}(d) 84 cm^{2}

**Question 8:**

What is the height of a cylinder of base radius as 1 cm and curved surface area as 88 cm^{2 }?

(a) 11 cm

(b) 14 cm

(c) 44 cm

(d) none of these

**Question 9:**

A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm. Its outer curved surface area is

(a) 1064.8 cm^{2
}(b) 1406.8 cm^{2
}(c) 1460.8 cm^{2
}(d) none of these

**Question 10:**

What is the curved surface area of a right circular cylinder of base radius 0.7 m and height 1 m ?

(a) 4.4 m^{2}

(b) 4.1 m^{2}

(c) 1.1 m^{2}

(d) none of these

**Answers**

1. (a)

2. (c)

3. (b)

4. (a)

5. (a)

6. (a)

7. (a)

8. (b)

9. (a)

10. (a)

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