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

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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 = 6a^{2}

#### 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 + πr^{2} = 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 r^{2}

Curved Surface Ares of a Hemisphere= 2πr^{2}

Total Surface Area of a Hemisphere = 3πr^{2}

#### 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 = a^{3}

#### 13.7 Volume of a Cylinder

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

Volume of a Cylinder = πr^{2}h

#### 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 =\(\frac{1}{3}\) πr^{2}h

#### 13.9 Volume of a Sphere

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

Volume of a Sphere =\(\frac{4}{3}\) πr^{3}

Volume of a Hemisphere = \(\frac{2}{3}\) πr^{3}

#### 13.10 Summary

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

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