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# RD Sharma Class 10 Chapter 16 Solutions (Surface Areas and Volumes)

RD Sharma Class 10 Maths Solutions Chapter 16 – Surface Areas and Volumes have been prepared by a team of experienced subject matter experts. In this chapter, you will learn the methods to determine the surface area and volume of combination solid objects formed by joining any two of the basic solids, such as cuboid, cone, cylinder, sphere and hemisphere. You will also learn that sometimes a new solid object can be formed by slicing an already existing solid object, for example, a frustum of the right circular cone is obtained from a cone by slicing its upper part.

In this chapter, there is a total of 95 questions asked in 3 exercises. All of these questions are intended to cover all the concepts taught in chapter 16 of RD Sharma Class 10 Maths Solutions Book. The questions given in this chapter enable you to have a deep insight into the concepts of three-dimensional geometrical figures. The questions ask you to determine the surface area and volume of objects formed by combining any two of the basic solids like cuboid, cone, cylinder, sphere and hemisphere. Some of the questions are based on frustum of right circular cone surface area and volume.

All of the questions asked in RD Sharma Class 10 Maths Surface Areas and Volumes have been answered comprehensively, accurately, and in an easy to understand step by step manner. They are just what you need to build a solid conceptual base, clear all your doubts and score high marks in your board exams.

## RD Sharma Class 10 Maths Surface Areas and Volumes: Important Topics

In Class 10 Maths Surface Areas and Volumes you learn that we come across a number of solids in our daily lives which are combinations of two or more of the basic solids. The basic solids are the cuboids, sphere, cone and cylinder. Further, you will learn here how to find the surface areas and volumes of combination objects made up of some basic solid figures. The concepts learnt in this chapter are discussed below.

• Surface Area of a Combination of Solids

Here you will learn that the strategy for the determination of the surface area of a combination solid starts with breaking down the figure into smaller solids of known type, and the total surface area (TSA) of the new solid is the sum of the curved surface areas (CSA) of each of the individual small solids. The smaller solids may be hemispheres, cones, and cylinders, among others. Here you also learn that while calculating the surface area, surface areas of the two constituents are not being added, because some part of the surface area disappears while joining them.

• The volume of a Combination of Solids

In this section, you will learn that the volume of the solid formed by joining two basic solid shapes is actually the sum of the volumes of the smaller constituent solid shapes.

• Conversion of Solid from One Shape to Another

In this part, you learn about some objects which are converted from one shape to another. For example, a liquid which originally filled one container of a particular shape is poured into another container of a different shape or size. Here you will learn to determine the volume of the two shapes.

• Frustum of a Cone

This portion teaches about ‘frustum’ of a cone which is a shape formed when we remove a portion of a right circular cone. Consider cutting with a knife, the upper pointed portion of a cone in such a manner that the line of cutting is parallel to the base of the cone. Remove the smaller cone from the upper portion to see the solid shape known as the frustum of the right circular cone, which has two circular ends with different radii.

Here are the various formulae involving the frustum of a cone.

(a) Volume of a frustum of a cone = 1/3 π h (r12 + r22 + r1 r2)

(b) CSA of a frustum of a cone = π l (r1 + r2), where l = √ [h2 + (r1 – r2)2]

(c) TSA of frustum of a cone = π l (r1 + r2) + π (r12 + r22); where h = vertical height of the frustum, l = slant height of the frustum r1 and r2 are radii of the two bases (ends) of the frustum.

### RD Sharma Class 10 Maths Chapter 16: Exercise-Discussion

There are total 3 exercises consisting of 95 questions in RD Sharma Class 10 Maths Chapter 16. The constituents of the exercises and types of questions asked are discussed below.

Exercise 16.1

There are 41 questions in this exercise. Questions 1 to 3 and 10 are based on the calculation of the volume of small spheres which combine to give a big sphere/cuboid. Questions 4 to 8 and 12 are constructed on the basis of the conversion of a big cylinder to a cylinder of smaller radius. Questions 9, 13 and 16 are based on the conversion of a big sphere to a cylinder of smaller radius. Question 11, 15 and 17 are based on the conversion of a sphere to a cone, and radius of the cone is to be determined. Question 14 is based on the conversion of a cylinder to the cuboid. Questions 18 to 41 are similar combinations to make more complex questions.

Exercise 16.2

This exercise consists of 37 questions. Question 1 to 3 and 5 asks you to determine the surface area and volume of solid objects made by the combination of a cylinder and a cone. Question 4 is based on parameters of a toy made by combining a cone and a hemisphere. Questions 6 to 37 are similar word problems based on the combination of various solid shapes with each other to give different physical objects.

Exercise 16.3

Here you will find 17 questions. All of these ask you to determine various parameters of the shape frustum of a right circular cone. The parameters needed to be determined include surface area, volume etc. for the different representation of this shape such as a bucket, milk container, reservoir etc.

### Benefits of RD Sharma Class 10 Maths Solutions for Chapter 16 – Surface Areas and Volumes

Some of the chief benefits of our smart and well-structured RD Sharma Class 10 Maths Solutions Chapter 16 – Surface Areas and Volumes are as given below-

• They are convenient, comprehensive, precise, fully accurate and user-friendly.
• All the questions have been answered in details and in a step by step manner to facilitate easy and effective learning.
• They follow a logical flow and give you enough practice of the various types of questions that can be asked in your Class 10 board exams.
• Our RD Sharma solutions are clear, effective, and help you improve your overall efficiency and speed.