• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

  • NCERT Solutions
    • NCERT Solutions for Class 12 English Flamingo and Vistas
    • NCERT Solutions for Class 11 English
    • NCERT Solutions for Class 11 Hindi
    • NCERT Solutions for Class 12 Hindi
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

Comparison of Curved Surface Areas and Total Surface Areas of Two Right Circular Cylinders Experiment Class 10 Maths Practical NCERT

The experiment to determine Comparison of Curved Surface Areas and Total Surface Areas of Two Right Circular Cylinders 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 Comparison of Curved Surface Areas and Total Surface Areas of Two Right Circular Cylinders Experiment

Determine Comparison of Curved Surface Areas and Total Surface Areas of Two Right Circular Cylinders Class 10 Practical

Objective
To compare the curved surface areas and total surface areas of two right circular cylinders which are formed from rectangular sheets of paper with same dimensions.

Prerequisite Knowledge

  1.  Construction of a cylinder from rectangular sheet by paper folding.
  2.  Area of rectangle = length X breadth
  3. Circumference and area of a circle.
    C=\(2\pi{r}\) , A = \(\pi {r}^{2}\)

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

Materials Required
Coloured glazed paper, sketch pens, a pair of scissors, fevicol, cellotape, geometry box.

Procedure

1. Take two rectangular sheets of paper of same dimensions as l= 14 cm and b =7 cm named as rectangle 1 and rectangle 2 .

NCERT Class 10 Maths Lab Manual - Comparison of Curved Surface Areas and Total Surface Areas of Two Right Circular Cylinders 1
2.Curve the rectangle 1 along its length l=14 cm.

3. Join two ends with cellotape to get a cylinder.

NCERT Class 10 Maths Lab Manual - Comparison of Curved Surface Areas and Total Surface Areas of Two Right Circular Cylinders 2
4. Similarly curve the rectangle 2 along its breadth b = 7 cm to get another cylinder as shown in figure.

NCERT Class 10 Maths Lab Manual - Comparison of Curved Surface Areas and Total Surface Areas of Two Right Circular Cylinders 3

Observation
For rectangle 1:
length of the rectangle = circumference of the circular base of the cylinder
l= \(2\pi {r}_{1}\)= 14 cm.
\({r}_{1}=\frac {14}{2\pi} =\frac {7}{\pi}\)
breadth of the rectangle = height of the cylinder
b = h = 7 cm.
curved surface area \({C}_{1}\quad \) = \(2\pi{r}_{2}{h}_{2}\) =
\(2\pi \times \frac {7}{2\pi } \times 14=98{cm}^{2}\)

Total surface area \({ T }_{ 1 }\quad =\quad 2\pi { r }_{1}^{2}\quad +\quad { C}_{1}\quad =\quad 2\pi \quad \times \frac { 49 }{ {\pi }^{ 2}} \quad +\quad 98\quad =\quad 98(\frac {1+\pi }{\pi })\)

For rectangle 2:
breadth of the rectangle = circumference of circular base of the cylinder
b=\(2\pi { r }_{ 2 }\) = 7 cm
\({r}_{2}\quad =\quad\frac {7}{2\pi}\)
length of the rectangle = height of the cylinder
l= \({ h }_{ 2 }\) = 14 cm.
curved surface area \({C}_{2}\quad =2\pi {r}_{2}{ h}_{2}\quad =\quad 2\pi \quad \times \frac { 7}{2\pi}\quad \times 14\quad =\quad 98\quad {cm}^{2}\)
Total surface area \(T_{ 2 }\quad =2\pi { r }_{ 2 }^{ 2 }\quad +{ C }_{ 2 }\)
=\(2\pi \times \frac {49}{ 4{\pi}^{2}}\quad +\quad 98\quad =49(\frac {1}{2\pi } +2)\quad =\quad 49(\frac { 1+4\pi}{\pi})\)

Result

  1. The curved surface areas (or lateral surface areas) of two cylinders of different height and radius formed from the two rectangular sheets of paper of same dimensions are same.
  2. The total surface areas of two cylinders of different height and radius formed from the two rectangular sheets of paper of same dimensions are not same.

Learning Outcome
Concept of comparison of curved surface area and total surface area of two cylinders formed from the two rectangular sheets of paper of same dimension is more clear. Students can understand easily that
\({C}_{1}={C}_{2}\) but \({T}_{1}\mp {T}_{2}\)

Activity Time

  1.  Take a rectangular sheet of paper of size 22 cm x 10 cm. Form two cylinders
    (i) curved along its length
    (ii) curved along its breadth.
    Compare the lateral surface areas and total surface areas of these two cylinders.

Question 1:
Find the height of a right circular cylinder made from a rectangle of length 15 cm and breadth 12 cm. It is curved along
its length.
Answer:
12 cm

Question 2:
What is the curved surface area of a cylinder obtained from a square of side 5 cm ?
Answer:
25 cm2

Question 3:
Radius ofthebaseofa paper cylinder is 7 cm and it is cut along its height. Find the length of the paper obtained.
Answer:
l= circumference of base = \(2\pi r=2\times\frac {22}{7} \times 7\) = 44 cm

Multiple Choice Questions

Question 1:
If the circumference of a circular base of a cylinder of height 2 cm is 132 cm, then the radius of the base is
(a) 21 cm
(b) 42 cm
(c) \(\frac {21}{2}\) cm
(d) none of these

Question 2:
A rectangular sheet of paper 44 cm X 18 cm is rolled along its length and a cylinder is formed. What will be the height of the cylinder ?
(a) 44 cm
(b) 18 cm
(c) 22 cm
(d) 9 cm

Question 3:
The area of a rectangular paper is 88 cm . Find its length if we obtain a circular cylinder of height 14 cm from it. [Hint : 27\(\pi\)rh =area of rectangle]
(a)  44 cm
(b) 88 cm
(c) \(\frac {44}{8}\)
(d) none of these

Question 4:
The diameter of a roller is 1.4 m and it is 2 m long. How much area will it cover in 2 revolutions ?
(a) 17.6 cm2
(b) 16.7 m2
(c) 61.7 m2
(d) none of these

Question 5:
The area of a circular base of a cylinder is \(\pi\) cm2and its height is 5 cm. Find the lateral surface area and .total surface area of the cylinder.
(a) 8\(\pi\) cm2,10\(\pi\)  cm2
(b) 10\(\pi\)  cm2, 12\(\pi\)  cm2
(c) 10\(\pi\) cm2, 10\(\pi\)  cm2
(d) none of these

Answers
1. (a)
2. (b)
3. (c)
4. (a)
5. (b)

Math LabsScience LabsScience Practical SkillsMath Labs with Activity

NCERT Class 10 Maths Lab Manual 

  • Determine Linear Equations Class 10 Experiment
  • Determine Basic Proportionality Theorem for a Triangle Class 10 Experiment
  • Determine Pythagoras Theorem Class 10 Experiment
  • Determine Ratio of Areas of Two Similar Triangles Class 10 Experiment
  • Determine Centroid of a Triangle Class 10 Experiment
  • Determine Arithmetic Progression I Class 10 Experiment
  • Determine Arithmetic Progression II Class 10 Experiment
  • Determine Sum of Odd Natural Numbers Class 10 Experiment
  • Determine Making of a Clinometer Class 10 Experiment
  • Determine Area of Circle by Coiling Method Class 10 Experiment
  • Determine Area of Circle by Paper Cutting and Pasting Method Class 10 Experiment
  • Determine Areas of Sectors formed at the Vertices of a Triangle Class 10 Experiment
  • Determine Tangents drawn from an External Point Class 10 Experiment
  • Determine Right Circular Cylinder Class 10 Experiment
  • Determine Right Circular Cone Class 10 Experiment
  • Determine Volume of a Cylinder Class 10 Experiment
  • Determine Volume of a Cone Class 10 Experiment
  • Determine Surface Area of a Cylinder Class 10 Experiment
  • Determine Surface Area of a Cone Class 10 Experiment
  • Determine Comparison of Curved Surface Areas and Total Surface Areas of Two Right Circular Cylinders Class 10 Experiment
  • Determine Comparison of Volumes of Two Right Circular Cylinders Class 10 Experiment
  • Determine Surface Area of a Sphere Class 10 Experiment
  • Determine Volume of a Sphere Class 10 Experiment
  • Determine Probability Class 10 Experiment

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers
  • The Summer Of The Beautiful White Horse Answers
  • Job Application Letter class 12 Samples
  • Science Lab Manual Class 9
  • Letter to The Editor Class 12 Samples
  • Unseen Passage For Class 6 Answers
  • NCERT Solutions for Class 12 Hindi Core
  • Invitation and Replies Class 12 Examples
  • Advertisement Writing Class 11 Examples
  • Lab Manual Class 10 Science

Recent Posts

  • Understanding Diversity Question Answer Class 6 Social Science Civics Chapter 1 NCERT Solutions
  • Our Changing Earth Question Answer Class 7 Social Science Geography Chapter 3 NCERT Solutions
  • Inside Our Earth Question Answer Class 7 Social Science Geography Chapter 2 NCERT Solutions
  • Rulers and Buildings Question Answer Class 7 Social Science History Chapter 5 NCERT Solutions
  • On Equality Question Answer Class 7 Social Science Civics Chapter 1 NCERT Solutions
  • Role of the Government in Health Question Answer Class 7 Social Science Civics Chapter 2 NCERT Solutions
  • Vital Villages, Thriving Towns Question Answer Class 6 Social Science History Chapter 9 NCERT Solutions
  • New Empires and Kingdoms Question Answer Class 6 Social Science History Chapter 11 NCERT Solutions
  • The Delhi Sultans Question Answer Class 7 Social Science History Chapter 3 NCERT Solutions
  • The Mughal Empire Question Answer Class 7 Social Science History Chapter 4 NCERT Solutions
  • India: Climate Vegetation and Wildlife Question Answer Class 6 Social Science Geography Chapter 8 NCERT Solutions
  • Traders, Kings and Pilgrims Question Answer Class 6 Social Science History Chapter 10 NCERT Solutions
  • Environment Question Answer Class 7 Social Science Geography Chapter 1 NCERT Solutions
  • Understanding Advertising Question Answer Class 7 Social Science Civics Chapter 7 NCERT Solutions
  • The Making of Regional Cultures Question Answer Class 7 Social Science History Chapter 9 NCERT Solutions

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions