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RD Sharma Class 9 Solutions Chapter 21 - Surface Area and Volume of Sphere (Ex 21.1) Exercise 21.1

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Last updated date: 13th Jun 2024
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Solutions to Chapter 21 for RD Sharma Class 9 Maths

Free PDF download of RD Sharma Class 9 Solutions Chapter 21 - Surface Area and Volume of Sphere Exercise 21.1 solved by Expert Mathematics Teachers on Vedantu. All Chapter 21 - Surface Area and Volume of Sphere Ex 21.1 Questions with Solutions for RD Sharma Class 9 Maths to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams. You can also register Online for Class 9 Science tuition on Vedantu to score more marks in your examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students.

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Class 9 Solutions Chapter 21 RD Sharma - Surface Area and Volume of Sphere (Ex 21.1) Exercise 21.1

Surface Area of Sphere

The surface area of a sphere refers to the area of the surface that resides on the sphere. When viewed as three-dimensional structures, circular shapes are most likely to appear as spheres. Take football, for example. You can get information on how to find the surface area of a sphere in this tutorial. Since spheres are three-dimensional objects, you will also learn about calculating the formula for the surface area of a sphere.


As a sphere is a solid object with a surface area of three, it is similar to a circle, but it differs from a circle in that a circle has a two-dimensional shape, while a sphere has a three-dimensional one.


The Formula of Surface Area of Sphere

In these circumstances, the formula of the surface area of a sphere is based on its radius. Let the radius of the sphere is r and the surface area is S. Therefore, the formula of the surface area of a sphere is as follows:

 

The surface area of a sphere is equal to \[4\pi r ^{2}\] , where r is its radius. It is also equal to \[4\pi \left ( \frac{d}{2} \right )^{2}\], where d is its diameter.


How to Calculate the Surface Area of Sphere?

It is possible to calculate the surface area of a sphere by applying the formula of the surface area of the sphere. The steps for calculating the surface area of a sphere are as follows:

Step 1: Calculate the radius of the sphere. 

 

Step 2: Multiply the radius square by itself. 

 

Step 3: Multiply the output of Step 3 by the approximate value of pi, which is 3.14. 

 

Step 5: Add the units to the final answer.


The Volume of Sphere

Spheres appear as round and 3-dimensional objects. They possess capacity. The volume of the sphere is defined in cubic units, such as m3, cm3 and in3. The sphere has round and 3-dimensional surfaces. There are three axes, and therefore three dimensions.


Since the sphere's cross-section is a circle, its volume depends on the diameter of its radius. A sphere’s surface area can be defined as the area or region of its outer surface. The volume of the sphere can be calculated if the radius r is given by the following  formula.


A sphere has a volume of \[\frac{4}{3}\pi r^{3}\]

 

How to Calculate Volume of Sphere?

A sphere's volume is the amount of space it occupies, and it can be calculated based on the formula above, which we already derived. To calculate the volume of a sphere, use the given steps:


When the diameter of a sphere is known, the radius can be determined by dividing the diameter by two. Find the cube of the radius r3 and multiply it by \[\frac{4}{3}\pi\].  

FAQs on RD Sharma Class 9 Solutions Chapter 21 - Surface Area and Volume of Sphere (Ex 21.1) Exercise 21.1

1. What are the key features of RD Sharma Solutions for Class 9 Maths Chapter 21?

Students can find solutions to all problems correctly based on their intelligence quotient with RD Sharma Solutions for Class 9 Maths Chapter 21. The solutions offer different approaches to solving tricky questions systematically and answer students’ doubts instantly while solving. In analyzing their readiness level, the students can work on the areas in which they need more practice. The textbook contains various sets of questions that will help the students to practice better. Answers to such questions are given in a detailed format so that students can grasp them easily. 

2. What is the meaning of the volume of Sphere according to RD Sharma Solutions for Class 9 Maths Chapter 21?

The volume of the sphere is the total area occupied by a sphere. A sphere can be formed by taking a circular disc, pasting a string along its circumference, and then rotating it along the string. The sphere has a volume of three-dimensional radius. It contains three axes, namely, x-axis, y-axis, and z-axis, which define its shape. Football and basketball are examples of spheres that have volume. The size of the sphere has to do with its radius or diameter since if we look at its cross-section, it is a circle. 

3. How are RD Sharma Solutions for Class 9 Maths Chapter 21 helpful from an exam perspective?

The chapter surface area and volume of the sphere is somewhat difficult than other chapters, thus this requires better understanding and continuous practice. A diligent approach to preparing these solutions helps students ace the final exams and top their class. RD Sharma Solutions for Class 9 Maths Chapter 21 is the most popular learning material used by students.  These solutions are designed according to the most up-to-date RD Sharma Solutions for Class 9 Maths Syllabus, covering all the important topics of the respective subject.

4. What is the Surface Area of Sphere according to chapter 21 of Class 9 Maths? Why is the Surface Area of a Sphere 4 Times the Area of a Circle?

In mathematics, the surface area of a sphere is equal to the total area of all its faces. It is always presented in square units. A sphere's surface area depends on its radius and diameter. It is expressed mathematically as 4πr2 square units. 


You can check whether the area of a sphere is four times more than that of a circle by wrapping a string around four circles whose surfaces are completely covered by a string. When we talk of the surface area of a sphere, we can write the surface area of a sphere as = 4πr2 = 4(πr2) = 4 × area of a circle.

5. What are the benefits of Referring to Vedantu Solutions for Exercise 1 of Chapter 21? 

The solutions provided by Vedantu are given by subject-matter experts of mathematics, thus the solutions given are accurate and explained step-by-step, to help students understand easily. The answers also include shortcuts and tricks wherever possible, thus saving the students time and effort during the exam. The other benefit of referring to the solutions is that you can also download them for future references and can have access to it from anywhere.