Xam Idea Class 10 Maths Chapter 13 Solutions: Surface Areas And Volumes

Xam Idea Class 10 Maths Solutions Chapter 13 ‘Surface Areas and Volumes’ have been created to assist you in solving the questions of the chapter easily. These Xam Idea solutions are created by our best subject experts and are in accordance with the latest CBSE Class 10 Maths Syllabus. The important topics covered in this chapter are the surface areas (including the lateral as well as the total surface area) of a combination of solids. You will get to solve mensuration problems based on the conversion of solids from one shape to another. Frustum of a Cone which carries a high weightage in the board exams is also covered in detail, in this chapter.

There are a total of 52 questions in this chapter divided into 6 exercises. These questions are categorized in such a manner that all the sections of the question paper of Class 10 board exams are covered thoroughly such as very short and short answer type questions, long answer type questions. The exercises, HOTS (Higher-order Thinking Skills) )and the value-based questions will help you gain complete conceptual clarity of the question-answer format if you solve these exercises extensively. Practising these questions is advised because the exercises in Xam Idea Class 10 Maths Chapter 13 – Surface Areas and Volumes cover the course in a detailed fashion and are suitable for quick revision right before your exams.

Our experts have created this set of Xam Idea Class 10 Maths solutions to address your doubts simultaneously while solving the questions. Such an approach to aid you in your self-study hours will also help you boost your efficiency of studying. We aim to provide you with a one-stop solution for all your queries related to Chapter 13 ‘Surface Areas and Volumes’ in the Xam Idea Class 10 Maths book. These solutions include some practical tips and tricks to approach the word problems related to surface areas and volume correctly. Teaming up with our platform for your self-study will help you achieve great marks in the board exams for sure.

Important Topics for Xam Idea Class 10 Maths Solutions Chapter 13: Surface Areas and Volumes

Surface Areas and Volumes 

  • You will learn about the differences between definitions and applications of the total surface area and curved surface area of a variety of solid objects such as a cuboid, cone, cylinder, sphere, and hemisphere and a combination of these shapes.
  • This chapter also covers the volume of the variety of objects formed by the combination of different solid shapes such as cuboid, cone, cylinder, sphere, and hemisphere. The volume of an object formed by combining any two of these will describe the amount of space occupied by them.
  • While evaluating the curved surface areas in the combination of solids we exclude the flat surfaces of the given solid.
  • In the evaluations of the total surface area in the combination of solids, we include all the faces of a given solid.

Some Important Formulae of Surface Areas and Volumes

  • Cuboid

If we consider a cuboid of dimensions l x b x h respectively.

Total surface area=2(lb+bh+hl)

Curved surface area=2(l+b) x h

volume=l x b x h

  • Cube

If we consider a cube of side a then,

Total surface area=6a2

Curved Surface area=4a2

The volume of a cube=a3

  • Right Circular Cylinder

If we consider a right circular cylinder of height h and radius r, then

Total Surface area=π2r(r+h)

Curved Surface area=π2rh


  • Right Circular Cone

Let us assume a right circular cone of height h, slant height l, and radius r, then

Total Surface area=πr(l+r)

Curved Surface area=πrl

Volume =

  • Sphere and Hemisphere

The surface area of the sphere with radius r=4πr2

The volume of a sphere

A hemisphere is the half of a sphere, therefore the formulae for the surface areas and volume of a hemisphere can be given as,

The curved surface area of a hemisphere=2πr2

The total surface area of a hemisphere=3πr2

The volume of a hemisphere

These formulae for hemispheres are obtained by dividing the formulae for the same situations in a sphere by 2.

You can use the above results and formulae suitably to find the surface area and volumes of the solid objects which are formed by the combination of these solid shapes.

The Frustum of a Cone

If we cut the tip of a given right circular cone, then the remaining portion is termed as a frustum. Now, considering a frustum of the cone with radius r1 and the radius of its upper circle as r2, then.

For the frustum,

Curved Surface Area = π (r1 + r2)l

Total Surface Area

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

Spherical Shell

The aspherical shell consists of two spheres in total. To find the volume of the solid portion in the given spherical shell with an external radius as r1 and internal radius as r2 respectively then, for the solid part of the shell,Note that throughout the chapter, we will considerunless it is stated otherwise.

Exercise Discussion of  Xam Idea Class 10 Maths Solutions Chapter 13: Surface Areas and Volumes

Very Short Answer Type Questions

This exercise consists of questions that will require minimalist answers. These questions are completely based on the formulae for the areas and volume of different solid shapes. You will be given with diagrams for aiding clarity in understanding the demand of the question. Some questions covered in this exercise include questions with a combination of solid shapes such as a cube combined with a hemisphere, or a double cone, etc.

Short Answer Type Questions

There are 2 exercises in this section. The questions in this section are word problems based on the measures of the frustum of the cone of which the volume or area is given. In some problems, you will be required to display a strong knowledge base in all the topics of this chapter.

Long Answer Type Questions

This exercise consists of complex problems in which you will get to evaluate the area and volume of shaded regions in given diagrams. To solve these questions, you will be required in-depth knowledge of the surface areas and volumes of different solid shape combinations

High Order Thinking Skills (HOTS)

In this exercise, there are advanced level questions that will help you build a strong foundational base with respect to the combination of solids. You will be required to find the radii of two spheres forming a shell, including the internal and external spheres both.

Value-Based Questions

The questions in this chapter are based on situational word problems such as the area occupied by tents in a camp for flood victims, number and rate of fencing around the garden, etc,

Why Use Xam Idea Class 10 Maths Solutions Chapter 13: Surface Areas and Volumes by Instasolv?

  • The question-answers that are given in these Xam Idea Class 10 Maths Solutions for Chapter 13 – Surface Areas and Volumes will clear your concepts of finding areas and volumes of different solids easily.
  • Understanding lengthy topics like these in a short yet detailed manner has been made possible by our meticulous mentoring team.
  • Our summary and solutions for Xam Idea are more descriptive than the textbook thus widening your range of knowledge and making you well prepared for any type of question in the exam.
  • We have explained each answer in compliance with the CBSE guidelines with a compromise in the quality of the solutions.
  • Using simple language is our trick to make the solutions inclusive and interactive for you.
  • Instasolv aims to provide a one-stop solution for all your queries and hence, our student-friendly platform is to complement these objectives.