# NCERT Exemplar Class 10 Maths Chapter 12 Solutions: Surface Areas and Volumes

NCERT Exemplar Class 10 Maths Solutions Chapter 12 ‘Surface Area and Volumes’ have been prepared to keep in mind the CBSE board exam guidelines. You will get complete guidance in solving the Exemplar exercise questions at Instasolv. The topics covered in this chapter of NCERT Class 10 Maths Exemplar are the total surface areas and curved surface areas of solid figures such as the hemisphere, frustum, solid sphere, and spherical shells. You will also be introduced to the formulae of evaluating the volume of all these solids.

There are a total of 4 exercises consisting of 29 questions of all kinds. There are short answer questions such as fill in the blanks or justification for statements that will push you to understand the topics in depth. The exercises also consist of long answer questions that carry high weightage in the question paper. Solving the NCERT Exemplar Maths Class 10 exercises will help you to prepare for various exams of your level such as CBSE Class 10 board exams and olympiads such as NTSE, RMO, etc..

We, at Instasolv, believe in providing you with answers that can be understood easily. Therefore, we have used simple student-friendly language in all the answers. Also, you will find that our NCERT Exemplar solutions are written in a step by step fashion to make the topics compatible with your conceptual understanding.

## Important Topics for NCERT Exemplar Class 10 Maths Solutions Chapter 12: Surface Area and Volumes

**Introduction**

- There are stark differences between definitions and applications of the total surface area and curved surface area of a solid object such as a cuboid, cone, cylinder, sphere, and hemisphere
- The volume of an object formed by combining any two of the basic solids such as cuboid, cone, cylinder, sphere, and hemisphere is the amount of space occupied by them.
- The curved surface area excludes the flat surfaces of a given solid.
- The total surface area covers all the faces of a given solid.

**Frustum of a Cone**

A frustum is a part of the cone such that the tip of the cone is cut off. If we consider a frustum of a cone with radius r_{1}and the radius of its upper circle as r_{2}, then

- Volume of the frustum = 1/3πh(r
_{1}^{2}+r_{2}^{2}+r_{1}r_{2}) - Curved Surface Area Of the Frustum=π(r
_{1}+r_{2})l - Total Surface Area Of the Frustum=π(r
_{1}+r_{2})l+πr_{1}^{2}+πr_{2}^{2}

Here,

such that h is the height of the frustum and l is the slant height of the given frustum.

**Hemisphere:**

- Curved Surface Area of a Hemisphere = 2πr
^{2} - Total Surface Area of a Hemisphere = 3πr
^{2} - Volume of a Hemisphere = 2/3πr
^{3}

If we consider that the radius of the given hemisphere is r. We can also get these results by relating a hemisphere to half of a sphere.

**Spherical Shell**

If we assume a spherical shell with radii r_{1}and r_{2}externally and internally respectively then,

For the solid part,

Note that throughout the chapter, we will consider π=22/7, unless it is stated otherwise.

### Exercise Discussion of NCERT Exemplar Class 10 Maths Solutions Chapter 12: Surface Area and Volumes

- Exercise 12.1 is objective in nature with a number of multiple-choice questions.
- Exercise 12.2 consists of mainly conceptual short answer type questions such as you will be required to justify the mathematical statements or check if a given statement is true or false with reasons.
- The third exercise 12.3 comprises 10 questions with a variety of polynomials so that you become proficient in finding the areas and volumes of solids.
- Exercise 12.4 consists of long answer type questions of miscellaneous nature, where you will require comprehensive knowledge of all the topics in this chapter.
- Solving these exercises thoroughly will help you stand out in other competitive exams of your level as well such as NTSE, olympiad, etc.
- You can get good marks in CBSE Class 10 board exams by practising the NCERT Exemplar problems.

### Why Use NCERT Exemplar Class 10 Maths Solutions Chapter 12: Surface Area and Volumes by Instasolv?

- The NCERT Class 10 Exemplar problem solutions for Maths Chapter 12 by experts at Instasolv are specially designed to help you with your homework and revision.
- These solutions at Instasolv will automatically enhance the efficiency of your self-study hours.
- Instasolv experts strictly comply with the latest CBSE guidelines and therefore, the answers prepared by them are very reliable.
- Instasolv solutions will clear all your basics related to surface areas and volumes chapter in an interactive manner.
- To score well in the exam, you should only look up to NCERT Solutions and NCERT Exemplar Class 10 Maths Solutions as they are self-sufficient and covers the entire syllabus of CBSE.