NCERT Solutions for Class 9 Maths Exercise 13.7 Surface Areas and Volumes updated for new academic session 2022-2023. All the questions are solved in Hindi and English Medium. Videos and PDF files are also given to download for offline use. Solutions are simplified in such a way every student can use it comfortably.
NCERT Solutions for Class 9 Maths Exercise 13.7
A right circular Cone and its Properties
As we have already mentioned above about the right circular cone. In Topic 13.7 you will study the volume of the cone. There is a massive similarity between the right circular cone and the pyramid. If we can be a little more liberal we say that a cone is another form of a pyramid.
The basic and only difference is that pyramid has a polygon (a square, pentagon or other) base, whereas, a right circular cone has a circular base. The tip of the cone is called the vertex or apex and the curved side is known as the lateral surface. Before diving deep into details, you must be comfortable with the concept of the volume of a cylinder.
Formula for the Volume of Cone
If you are not well versed with the concept of cylinder, you might find it a little difficult to understand. Though, you have already studied about the surface area of a right circular cone. Here is the formula of the cone V = 1/3 πr^2h and surface area formula is πr^2 + πrl. The thing to notice here, r, h, and l, shows different a measurement.
The r shows the radius of the base of the cone, h shows the height and l is for slant height of the cone. More specifically, the height determined by that line which goes from the middle of the base to the vertex. For the slant height, you can imagine the line that goes from the vertex of the cone to the edge of the base.
Application of Formula of Volume of Cone
If all the dimensions are given for any particular question, just put the value in the formula to get the answer. In most of the questions you have to solve the volume and surface area equation by replacing the measurement in formulae variables.
Questions based on volumes are easier than that of surface areas. To understand the concept completely you have to compare it with cylinder-like objects. It is done in the figure of explanation 13.7 also. This will show you a clear picture of how there is a difference between height and slant height.
Finding Volume of Cone in Exercise 13.8
To understand the derivation of these formulae one must see the activity. If you fill the cone with liquid and emptied in the cylinder, it will take three times to fill the cylinder with the liquid.
That is why the volume of cone is just one-third of the cylinder. The cylinder has a parallel side and congruent base that makes it bigger than the cone. However, the slant height is only used in the pyramid and cone. There are certain facts to be remembered – there are two distinct types of cones, the right circular conical and the irregular one.
It is based on the placement of the apex in combination with the base. The entire space that is covered by this type of 3D object is determined by the volume of the right circular cone.