Courses
Courses for Kids
Free study material
Offline Centres
More
Store

Cylinder, Cone and Sphere Solutions for ICSE Board Class 10 Mathematics

Last updated date: 04th Aug 2024
Total views: 791.7k
Views today: 12.91k

Cylinder, Cone and Sphere (Surface Area and Volume) Solutions for ICSE Board Class 10 Mathematics (Concise - Selina Publishers)

Free download of step by step solutions for class 10 mathematics chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume) of ICSE Board (Concise - Selina Publishers). All exercise questions are solved & explained by an expert teacher and as per ICSE board guidelines.

Competitive Exams after 12th Science

Let’s have a Brief Overview of Cylinder, Cone and Sphere

Cylinder

A cylinder is a three-dimensional solid figure, it is one of the most fundamental of curvilinear geometric shapes (from Greek: o, romanized: Kolindros, lit. 'roller', 'tumbler'. From a geometric point of view, it is a prism with a circle as its basis.

This conventional viewpoint is still used in basic geometric treatments, but sophisticated mathematical viewpoints have switched to the infinite curved surface, which is how a cylinder is currently described in different modern fields of geometry and topology.

We have all seen a cylinder; now let's learn how to define one in scientific terms. It is a solid figure with straight and parallel sides and a circular or oval base or cross-section. It is a solid closed form with two circular bases joined by a curved surface. A cylinder can be considered a limiting case of a prism.

Cone

A cone is a solid three-dimensional geographic feature with a flat circular (or roughly circular) base that tapers smoothly to the vertex or tip. As a result, the cone is created by a solid generated by a line with one end fixed (apex) and the other describing a closed curve on a plane.

The cone does not extend beyond the base of line segments, although it does extend infinitely far in the case of half-lines. When it comes to lines, the cone can extend indefinitely in both directions from the apex, which is known as a double cone. A nappe is one half of a double cone on one side of the apex.

Sphere

A sphere is a solid round three-dimensional shape with equal distances between all points on its surface. As a result, a sphere's radius is all equal. A football, basketball, or other sphere is the finest example. The hemispheres are formed when a large circle divides the sphere into two equal pieces. The longest straight line segment joining two locations on the sphere travels through the centre, and its length is thus twice the radius; it is the diameter of both the sphere and its ball.

FAQs on Cylinder, Cone and Sphere Solutions for ICSE Board Class 10 Mathematics

1. What are some important formulae of a cylinder?

We call it a Right Cylinder when the producing line is perpendicular to the base. However, an oblique cylinder is one in which one of the bases appears sideways, i.e. not perpendicular to the base. Let's look at some of the most significant formulas now.

• The volume of a cylinder = Area of base × Height of cylinder = πr²h

• The Lateral Surface Area (LSA) = Perimeter of base × height = 2πrh = πdh

• The Total Surface Area (TSA) = The Lateral Surface Area (LSA) + Area of bases = 2πrh + 2πr² = 2πr (h+r)

To know more about Cylinder, Cone and Sphere - you can click on Cylinder, Cone and Sphere Solutions for ICSE Board Class 10 Mathematics.

2. What are the formulas of a hollow cylinder?

Another element of cylinders that we need to understand is a hollow cylinder, such as a pipe. The formulas will alter significantly in this case. There are two radii to remember here: R for the outer cylinder and r for the inner cylinder.

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

• The Lateral Surface (hollow cylinder) = The External Surface Area + The Internal Surface Area = 2πRh + 2πrh = 2π(R+r)h

•  The Total Surface Area (cylinder) = The Lateral Area = The Area of bases = 2π(R+r)h + 2π (R² – r²) h

3. What are the important formulae of a cone?

A cone is a solid three-dimensional geographic feature with a flat circular (or roughly circular) base that tapers smoothly to the vertex or tip. Therefore, the cone is made by a solid generated by a line with one end fixed and the other describing a closed curve on a plane. Let's have a look at some cone formulas.

• Volume of a cone = 13 area of base × height = 13 πr²h

• Lateral Surface = 12 radius × arc length = 12 l × 2πr = πrl

• where l = slant height = √(r² + h²)

• Total Surface Area (TSA) = lateral surface area (LSA) + Area of base = πrl + πr²

4. What are some important formulae of a sphere?

A sphere is a solid round three-dimensional shape with equal distances between all points on its surface. As a result, a sphere's radius is all equal. A football, basketball, or other sphere is the finest example. The hemispheres are formed when a large circle divides the sphere into two equal pieces. Let's have a look at the most important formulas.

• The Surface Area of a Sphere (TSA) = 4 times of its great circle = 4πr² = πd²

• The Volume of a Sphere = 43 πr² = π6 d³

5. How to prepare the topic of Cylinder, Cone and Sphere of Class 10 Mathematics?

Firstly, students need to learn the basic properties of the cylinder, cone and sphere. They need to possess strong fundamentals about all the three figures, i,e, cylinder, cone and sphere. Then, they need to be thorough with the formulas related to the cylinder, cone and sphere. It would be a huge advantage for the students if they can learn how the formulas are derived. As that would cement the formulas more firmly in their mind. Finally, practice is very important for students to ace the exams. Students can always try to solve the sample papers related to the exam. Students can check out the Vedantu app and website which has free study materials.