 # NCERT Solution for Class 9 Maths Chapter 13 Free PDF Download

## NCERT Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volumes

For every student, math is the most difficult subject and CBSE recommends NCERT books which are not sufficient. But these books are necessary for studies. Also, the students need to solve all the question and answer given in the exercise to completely learn the topic. Toppr provides the best NCERT Solutions for Class 9 Maths Chapter 13.

Our NCERT Solutions for Class 9 Maths Chapter 13 is outlined for the students according to the latest CBSE board exam guideline and course of study. These solutions will help you to score good marks in your boards. You can find all the NCERT solution for class 9 maths chapter 13 in a single place.

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### CBSE Class 9 Maths Chapter 13 – Surface Areas and Volumes NCERT Solutions

Surface areas refer to a material that covers a geometric solid. On the other hand, volume refers to the measure of how much a figure can hold and it is measured in cubic units. ### Sub-topics covered under NCERT Solutions for Class 9 Maths Chapter 13

#### 13.1 Introduction

This topic describes what is plane figure and what is a solid figure.

• Plain Figures- Refers to those figures that are 2D and consist of length and breadth.
• Solid Figures- Refers to those figures that are 3D and consist of length, breadth, and height.

#### 13.2 Surface Ares of a Cuboid and a Cube

A cube is a 3D square and a cuboid is a 3D rectangle. This topic with the help of an example explains how to find the area of a cuboid.

Surface Area of a Cuboid = 2 (lb + bh + hl)

Surface area of a Cube = 6a2

#### 13.3 Surface Area of a Right Circular Cylinder

A Cylinder can be understood as a circular prism. This topic also explains how to find the surface area of a right circular cylinder with the help of an example

Curved surface area of a Cylinder = 2πrh

Total surface area of a Cylinder = 2πr(r+h)

#### 13.4 Surface Area of a Right Circular Cone

A cone can be called a cylinder with a pointy edge on one side. This topic also with the help of an example explains how to find the Area of Right Circular Cone.

Curved Surface Area of a Cone = $$\frac{1}{2}$$ × l ×2πr = πrl

Total Surface Area of a Cone = πrl + πr2 = πr (l + r)

#### 13.5 Surface Area of a Sphere

A Sphere is a complete round circle and hemisphere is the half of sphere. In this topic also the way of finding Area of a Sphere is discussed with the help of an example.

Surface Area of a Sphere = 4 π r2

Curved Surface Ares of a Hemisphere= 2πr2

Total Surface Area of a Hemisphere = 3πr2

#### 13.6 Volume of a Cuboid

This topic tells how to find volume of a cuboid and cube

Volume of a Cuboid = base area × height = length × breadth × height

Volume of a cube = edge × edge × edge = a3

#### 13.7 Volume of a Cylinder

This topic tells how to find the volume of a cylinder.

Volume of a Cylinder = πr2h

#### 13.8 Volume of a Right Circular Cone

This topic tells the formula of finding the volume of a right circular cone

Volume of a Right Circular Cone =$$\frac{1}{3}$$ πr2h

#### 13.9 Volume of a Sphere

This topic tells how to find the volume of a sphere and hemisphere.

Volume of a Sphere =$$\frac{4}{3}$$ πr3

Volume of a Hemisphere = $$\frac{2}{3}$$ πr3

#### 13.10 Summary

This topic contains all the areas and volume that we have discussed in this chapter.

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