RD Sharma Class 9 Maths Surface Area and Volume of A Right Circular Cone Solutions - Free PDF Download
FAQs on RD Sharma Solutions for Class 9 Maths Chapter 20 - Surface Area and Volume of A Right Circular Cone
1. What are the key formulas from RD Sharma Chapter 20 for calculating the surface area and volume of a right circular cone?
To solve problems in RD Sharma Chapter 20, you must know these essential formulas for a right circular cone with radius 'r', height 'h', and slant height 'l':
- Curved Surface Area (CSA) = πrl
- Total Surface Area (TSA) = πr(l + r)
- Volume (V) = (1/3)πr²h
The slant height can be found using the Pythagorean theorem: l = √(r² + h²).
2. How do you find the slant height (l) of a cone if only the radius (r) and height (h) are given in an RD Sharma problem?
In many RD Sharma problems, the slant height (l) is not directly provided. You can calculate it by applying the Pythagoras theorem to the right-angled triangle formed by the cone's height (h), radius (r), and slant height (l). The formula is l = √(r² + h²). Always calculate the slant height first if you need to find the Curved or Total Surface Area.
3. What is the step-by-step method to solve problems asking for the Total Surface Area (TSA) of a cone in RD Sharma Class 9?
To find the Total Surface Area (TSA) of a cone accurately, follow these steps as per the methods in RD Sharma:
- Identify the given values: radius (r) and height (h) or slant height (l).
- If the slant height (l) is not given, calculate it using the formula l = √(r² + h²).
- Calculate the area of the circular base using the formula A_base = πr².
- Calculate the Curved Surface Area (CSA) using the formula CSA = πrl.
- Add the base area and the CSA to get the TSA: TSA = A_base + CSA, which simplifies to TSA = πr(r + l).
- Ensure your final answer is in the correct square units (e.g., cm² or m²).
4. If a question in RD Sharma Chapter 20 describes a conical tent, which surface area formula should be used and why?
For a question about a conical tent, you should use the formula for the Curved Surface Area (CSA = πrl). This is because a tent is open at the bottom and does not have a circular base made of canvas. The Total Surface Area (TSA) formula would incorrectly include the area of the ground, which is not part of the tent's material.
5. Why is it incorrect to use the formula for the volume of a cylinder when calculating the volume of a cone? How are the two formulas related?
It is incorrect because a cone and a cylinder with the same base radius and height have different capacities. The volume of a cone is exactly one-third the volume of a cylinder with the same base radius (r) and height (h).
- Volume of Cylinder = πr²h
- Volume of Cone = (1/3)πr²h
This relationship is crucial for solving comparison problems often found in RD Sharma, where you might be asked to find how many cones can be filled from a cylinder.
6. How does identifying the different surfaces of a right circular cone help in correctly applying the surface area formulas from RD Sharma?
A right circular cone has two distinct surfaces: a flat circular base and a curved surface. Understanding this is key to choosing the correct formula for a problem.
- If a problem asks for the area of material needed for an object like an ice cream cone or a tent, it refers only to the Curved Surface Area (CSA = πrl).
- If the problem involves a solid, closed object like a wooden toy, it requires the Total Surface Area (TSA = πr(r + l)), which includes both the curved surface and the circular base.
7. In complex problems from RD Sharma, how do you calculate the cost of canvas required to make a conical tent if the rate per square metre is given?
To solve such practical problems, follow these steps:
- First, determine the surface area of the canvas needed. Since it's a tent, this will be the Curved Surface Area (CSA).
- Calculate the CSA using the formula CSA = πrl. Ensure your radius and slant height are in metres if the cost is per square metre.
- Once you have the CSA in square metres, calculate the total cost by multiplying this area by the given rate.
- The formula is: Total Cost = CSA × Cost per m².
8. What is a common mistake students make when finding the volume of a cone derived from a solid cylinder of the same dimensions?
A very common mistake is forgetting to divide by three. Students often calculate the volume of the corresponding cylinder (πr²h) and present that as the answer. Always remember that the volume of a cone is one-third of the volume of a cylinder with an identical base and height. The correct formula is V = (1/3)πr²h. This is a frequent source of error in exams.
