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

NCERT Solutions for Class 9 Maths Chapter 13 Surface Area and Volumes: The concepts of this chapter is used in our daily life for calculations like how many liters of paint needed to paint an entire house? how much box is needed to fill these chocolates? what should be the area of the sheet I should by to cover the roof of my house? These types of calculations can be done using the concept of surface areas and volumes. In construction works and many other fields, many calculations are done using the concept of NCERT Solutions for Class 9 Maths Chapter 13. So the chapter is very important in daily life and also for the exams. There are many interesting questions mentioned in the NCERT Solutions for Class 9 Maths of this chapter. You will study surface areas and volumes of cuboid, right circular cylinder, right circular cone and sphere in the NCERT solutions of this chapter.

A cuboid looks like a bundle of thin papers. Suppose the length of the paper is l and breadth is b then the area of the paper is lb and if the height of the bundle is h then the volume of the bundle is lbh. That is if the length of a cuboid is l, breadth is b and height is h then the area is lbh. What is the area of the sheet required to cover the cuboid?

There are two surfaces with area lb, lh, and bh. Then the total area of the sheet required to cover the cuboid is 2(lb+bh+lh) and this area is called the surface area of a cuboid. Suppose l=b=h then it will be a cube and area of the cube is a3 and surface area is 6a2.

The next body mentioned in the NCERT Solutions for Class 9 Maths Chapter 13 is the right circular cylinder. If you stack a thin circular sheet of paper vertically then it will form a right circular cylinder.

The area of a single circular sheet is $\pi r^2$ and if the height of the stack is h then the volume of the cylinder is $V=\pi r^2 h$ where r is the radius of the circular sheet. Now if we have to cover the right circular cylinder except base and top then the area of sheet requires will be $2\pi r h$ and is called a curved surface area of the cylinder. And if we have to cover top and base also then the total surface area of the right circular cylinder is $\pi r^2+\pi r^2+2\pi r h=2\pi r(r+h)$.  The other bodies mentioned in the NCERT Solutions for Class 9 are a right circular cone, solid sphere, and hemisphere.

The main topics of the NCERT Solutions for Class 9 Maths Chapter 13 Surface Area and Volumes are given below

13.1 Introduction

13.2 Surface Area of a Cuboid and a Cube

13.3 Surface Area of a Right Circular Cylinder

13.4 Surface Area of a Right Circular Cone

13.5 Surface Area of a Sphere

13.6 Volume of a Cuboid

13.7 Volume of a Cylinder

13.8 Volume of a Right Circular Cone

13.9 Volume of a Sphere

The concept of surface area and volumes are explained in detail with figures and explanation and interesting questions are given in NCERT book.

## NCERT Solutions for Class 9 Maths - Chapter Wise

 Chapter No. Chapter Name Chapter 1 Number Systems Chapter 2 Polynomials Chapter 3 Coordinate Geometry Chapter 4 Linear Equations In Two Variables Chapter 5 Introduction to Euclid's Geometry Chapter 6 Lines And Angles Chapter 7 Triangles Chapter 8 Quadrilaterals Chapter 9 Areas of Parallelograms and Triangles Chapter 10 Circles Chapter 11 Constructions Chapter 12 Heron’s Formula Chapter 14 Statistics Chapter 15 Probability