RD Sharma Class 9 Chapter 20 Solutions (Surface Area And Volume of A Right Circular Cone)
RD Sharma Solutions for Class 9 Maths Chapter 20 is the perfect reference book to learn and understand all the concepts of Surface Area and Volume of a Right Circular Cone. There are 63 questions in this chapter of RD Sharma Solutions and a total of 4 exercises. They brush up your knowledge on important definitions and formulas on the right circular cone-like its volume, curved surface area, and total surface area. This is a very useful topic since we come across a lot of conical-shaped things in our day to day life.
Based on CBSE Syllabus, many of the questions in this book could actually appear in your exams. Solving these questions by referring to our solutions will further give you clarity on this topic. Our subject matter experts break down every solution into simple and smaller steps for a clear and detailed explanation.
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Important Topics for RD Sharma Solutions for Class 9 Chapter 20: Surface Area and Volume of a Right Circular Cone
A 3D figure with a circular base and a curved surface, which tapers gradually towards a point just above the base, is a cone. A right circular cone is where the axis of the cone is perpendicular to the radius of the base circle.
When you revolve a right angle triangle on one of its sides (either base or height), it forms a solid which is the right circular cone.
The following definitions and formulas related to a right circular cone will be used extensively to solve all the problems:
- Apex or Vertex – The point above the circular base where the straight lines (which form sides of the cone) meet is called its apex or vertex.
- Axis – The straight line that joins the vertex to the midpoint of the circular base is called its axis. It forms a right angle with the radius of the circular base.
- Frustum – If you cut off a circular cone by a plane parallel to the base, the portion of the cone which is between the base and the parallel plane cutting it is called a frustum.
- Height of the cone – The length of the line which connects the vertex to the centre of the base is taken as the height of the cone.
- The slant height of the cone – The distance along the lateral face of a cone, from the base to the vertex is its slant height.
- If a right circular cone has a base with radius r, height h, and slant height l, then:
- Slant height formula – Since the slant height is also the hypotenuse of the right triangle you can calculate it using Pythagoras theorem Slant height = √r2 + h2
- Curved surface area – Since the base of the cone is a circle, the lateral or curved surface area is given by Lateral area = πrl
- Total surface area – The sum of the area of the base and the lateral surface area gives the total surface area of the Cone. Total surface area = πrl + πr2
- Volume – One-third of the area of base multiplied with height gives the volume of a right circular cone. Volume = 1/3 * base * height = 1/3 * πr2 * h
- Few important things to remember about a right circular cone
- Its base is circular and its axis, that joins the centre of the circle with the apex, is perpendicular to the circle.
- When you form a triangle by joining the cone’s apex with 2 points on the outside of the base circle it would be an isosceles triangle.
Exercise Discussions of RD Sharma Solutions for Class 9, Chapter 20: Surface Area and Volume of a Right Circular Cone
- There are 23 questions in the first exercise. In these, you need to find the curved surface area or the curved surface area is given and height or radius is to be calculated. There are questions on calculating total surface area, word problems involving 2 cones, and finding the ratio between their heights or radii.
- There are 15 questions in RD Sharma Class 9 Maths Solutions the 2nd exercise which is mostly on finding the volume of a right circular cone. Some problems involve 2 cones with some relationship between their different values and one has to find ratios of their other values.
- The 3rd exercise has 8 questions which are VSAQs or very short answer questions. In some questions the volume and height are given and you need to find radius and diameter or height and slant height is given and you need to find out its volume. There are few questions on the lateral and total surface area.
- There are 17 questions in the 4th set which are objective type questions. Most of the questions are pretty straight forward that require you to just use definitions and theorems to answer them. Questions in the exercise give you a good round-up of all the learned concepts and formulas.
Benefits of RD Sharma Solutions for Class 9, Chapter 20: Surface Area and Volume of a Right Circular Cone
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