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Surface Area of a Cylinder Experiment Class 10 Maths Practical NCERT

The experiment to determine Surface Area of a Cylinder are part of the Class 10 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 10 CBSE Surface Area of a Cylinder Experiment

Determine Surface Area of a Cylinder Class 10 Practical

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

Prerequisite Knowledge

  1. Area of a rectangle.
  2.  Area of a circle.
  3.  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

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

NCERT Class 10 Maths Lab Manual - Surface Area of a Cylinder 1
Observation

  1. 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
  2.  Length of rectangle = circumference of base of cylinder = \(2\pi \)r
  3.  Breadth of rectangle = height = h
  4.  Area of rectangle = \(\pi { r }\)x h = curved surface area of cylinder
  5.  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.
NCERT Class 10 Maths Lab Manual - Surface Area of a Cylinder 2

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 cm3

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 cm2. 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  m2 . 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 m2
(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 cm2. 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 cm2 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 cm2
(b) 80 cm2
(c) 82 cm2
(d) 84 cm2

Question 8:
What is the height of a cylinder of base radius as 1 cm and curved surface area as 88 cm2 ?
(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 cm2
(b) 1406.8 cm2
(c) 1460.8 cm2
(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 m2
(b) 4.1 m2
(c) 1.1 m2
(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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NCERT Class 10 Maths Lab Manual