Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# ICSE Class 10 Mathematics Revision Notes Chapter 20 - Cylinder, Cone and Sphere

Last updated date: 18th Sep 2024
Total views: 676.8k
Views today: 8.76k

## Revision Notes for ICSE Class 10 Maths Chapter 20 - Free PDF Download

Free PDF download of Class 10 Mathematics Chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume) Revision Notes & Short Key-notes prepared by our expert Math teachers as per ICSE guidelines. To register Maths Tuitions on Vedantu.com to clear your doubts.

It is one of the most important topics to concentrate on for ICSE Class 10 students. Students will learn how to find the surface area and volume of cylinders, cones, and spheres, convert solids and combine solids, and solve miscellaneous problems. The revision notes are prepared in a way that students can clarify their doubts on the site to their convenience, as well as get guidance on how to solve problems confidently. Therefore, improving their problem-solving abilities, which are crucial for exams.

Competitive Exams after 12th Science

## Revision Notes for ICSE Class 10 Maths Chapter 20 - Cylinder, Cone and Sphere

### Cylinder

Cylinders are solid figures with a circular base or cross-section and parallel sides. They are closed solid figures formed by two circular bases and connected by a curved surface. It is a solid figure that consists of two circular bases connected by smooth, curved surfaces. Cylinders have a circular cross-section and parallel sides and are closed solid figures.

• Volume of a cylinder = Base Area * Height of cylinder= πr²h

• Lateral Surface Area = Base Perimeter × height = 2πrh = πdh

• Total Area = Lateral Surface + Base Area= 2πrh + 2πr² = 2πr (h+r)

Additionally, the chapter teaches students how to solve problems for hollow cylinders, such as pipes, which utilize slightly different formulas.

In this case, we have to keep two radii in mind: R for the outer cylinder, and r for the inner cylinder:

• Hollow Cylinder Volume = Volume of External Cylinder - Volume of Internal Cylinder= πR²h – πr²h = π (R² – r²) h

• Internal Surface Area + External Surface Area (Hollow Cylinder)= 2πRh + 2πrh = 2π(R+r)h

• A Total Surface Area (Cylinder) = A lateral surface area = A base surface area= 2π(R+r)h + 2π (R² – r²) h

### Cone

The cone, as a solid three-dimensional figure, comprises a flat circle with a smooth taper to a point known as the vertex or apex. It is formed by a line with one point fixed (apex) and another fixed (base).

• Total cone surface area = πr2 + πrl = πr (r + l).

• A cone's volume is πr2h3

### Sphere

Spheres are solid round three-dimensional figures with every point on their surfaces equidistant from their center. A sphere is best illustrated by footballs, basketballs, etc. A sphere is bifurcated into two equal parts by great circles.

• The surface of a sphere is equal to 4πr2

• A sphere has a volume equal to 4/ 3πr3

## FAQs on ICSE Class 10 Mathematics Revision Notes Chapter 20 - Cylinder, Cone and Sphere

1. According to concepts taught in chapter 20 of ICSE Class 10 Maths, solve this:A circular cylinder has a height of 20 cm and a radius of 7 cm. (i) Calculate the volume  and (ii)surface area

To attempt this type of question, you need to make sure that you know each and every formula and also have an idea of how to and where to apply the formula.

For Instance, For a Given Question The Formula Can Be Applied As:

• Considering a circular cylinder of height h = 20 cm and radius r = 7 cm (i) Volume of cylinder = r2h = 22/7 x 72 x 20 cm3= 3080 cm3

• The area of a cylinder is equal to 2πr (h + r)= 2 x 22/7 x 7(20 + 7) cm2= 2 x 22 x 27 cm3= 1188 cm3

2. According to concepts taught in chapter 20 of ICSE Class 10 Maths, to cast a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long from a solid cylinder of diameter 2 cm, how much length must be added?

Since the external diameter of the hollow cylinder is 20 cm,

There is a radius of 10 cm equal to R.

The thickness is 0.25 cm.

Therefore, the internal radius = (10 – 0.25 = 9.75 cm = r)

The length of the cylinder (h) is 15 cm

Now,

Volume = πh (R2 – r2) = π x 15(102 – 9.752) = 15 π (100 – 95.0625)

= 15 π x 4.9375 cm3

Now,

Solid cylindrical diameter = 2 cm

Therefore, radius (r) = 1 cm, length (h) = 1 cm and volume (V) = πr2h = πh cm3

Accordingly, based on the condition given in the question

πh = 15 π x 4.9375

h = 15 x 4.9375

h = 74.0625

Therefore, the length of the solid cylinder is 74.0625 cm

3. According to concepts taught in chapter 20 of ICSE Class 10 Maths, solve the following:

A cylindrical shape has a diameter of 20 cm. Its radius is 100 sq cm.

Find:

• The cylinder dimensions are correct to one decimal place.

• The volume is also correct to one decimal place.

Given,

The cylinder's diameter is 20 cm

So, the radius (r) = 10 cm

surface area = 100 cm2

Height = h cm

(i) Curved surface area = 2πrh

So,

2πrh = 100 cm2

2 x 22/7 x 10 x h = 100

h = (100 x 7)/ (22 x 10 x 2) = 35/22

h = 1.6 cm

(ii) Volume of the cylinder = πr2h

= 22/7 x 10 x 10 x 1.6

= 502.9 cm3

4. How will Revision Notes help you score well for class 10 ICSE Maths?

Revision Notes Help You Score Well For Class 10 Icse Maths In The Following Ways:

• Saves Time: All the concepts from the chapter are summarized here in one document so that students can review them quickly. This saves students time and energy searching for formulas and concepts. All formulas and concepts for each chapter have been extracted here into a single note.

• These notes have been designed by subject experts with an emphasis on simplicity and precision, covering almost all areas such as cylinder, cone and sphere.

• These notes along with the  sample papers available at vedantu are detailed and could assist students in getting good marks in their 10th standard as well as their post-secondary education.

5. Why should one write notes for Mathematics class 10th ICSE paper?

One Should Write Notes For Mathematics Class 10th Icse Paper For The Following Reasons:

• Creating handwritten notes is always considered the best way to truly grasp the concept and score well on an exam.

• When it comes to Class 10th Maths, there is no denying that it is considered as one of the toughest subjects in your curriculum, thus having notes by your side is an all-time essential.

• Class 10th Maths is full of numerical, graphs and formulas thus making your own notes and highlighting them is the only way you can catch hold of them.

• If students want to be able to develop their answering capacity and speed during the exam, they should make their own revision notes.

• Having handy notes means better revision and better revision means the best result so make sure you prepare your own notes.