RD Sharma Class 9 Solutions Chapter 20 - Surface Area and Volume of Right Circular Cone (Ex 20.2) Exercise 20.2 - Free PDF
FAQs on RD Sharma Class 9 Solutions Chapter 20 - Exercise 20.2
1. Based on RD Sharma solutions, what is the first step to find the volume of a cone if only its radius (r) and slant height (l) are given?
The first and most crucial step is to calculate the perpendicular height (h) of the cone. The formula for the volume of a cone, V = (1/3)πr²h, requires the perpendicular height, not the slant height. You must use the Pythagorean theorem in the form h = √(l² - r²) to find 'h' before you can apply the volume formula.
2. What is the correct formula for the Total Surface Area (TSA) of a cone as used in Chapter 20 solutions?
The Total Surface Area (TSA) of a right circular cone represents the sum of its Curved Surface Area (the slanted part) and the area of its circular base. The formula is TSA = πrl + πr², which is often simplified to TSA = πr(l + r), where 'r' is the radius of the base and 'l' is the slant height of the cone.
3. How do you determine whether a problem requires calculating the Curved Surface Area (CSA) or the Total Surface Area (TSA) of a cone?
You can decide which formula to use by carefully reading the problem's context.
- Use Curved Surface Area (CSA = πrl) when the problem concerns only the lateral surface and excludes the base. A common example is calculating the amount of canvas needed for a conical tent.
- Use Total Surface Area (TSA = πr(l + r)) when the problem requires the area of all surfaces of a solid object, including the circular base. An example would be finding the total area to be painted on a solid cone-shaped block.
4. Why is the Pythagorean theorem (l² = r² + h²) essential for solving problems on the surface area and volume of a cone?
The Pythagorean theorem is essential because the radius (r), perpendicular height (h), and slant height (l) of a right circular cone form a right-angled triangle, with the slant height as the hypotenuse. Often, a problem will only provide two of these three dimensions. To calculate surface area (which needs 'l') or volume (which needs 'h'), you frequently need to use this theorem first to find the missing third dimension.
5. What are the key steps to calculate the volume of a cone, following the method in RD Sharma Class 9 solutions for Exercise 20.2?
The key steps to calculate the volume of a right circular cone are as follows:
- Identify Given Values: Note the radius (r) and perpendicular height (h) provided in the problem.
- Calculate Missing Dimensions: If the slant height (l) is given instead of 'h', use the formula h = √(l² - r²) to find the perpendicular height.
- Apply the Volume Formula: Substitute the values of 'r' and 'h' into the volume formula, V = (1/3)πr²h.
- State the Final Answer: Compute the result and write the answer with the correct cubic units (e.g., cm³ or m³).
6. How is the volume of a cone related to the volume of a cylinder with the same base and height?
The volume of a cone is exactly one-third the volume of a cylinder that shares the same base radius (r) and perpendicular height (h). This fundamental relationship, V_cone = (1/3) × V_cylinder, is a key concept in mensuration. It means you would need to fill a cone with a substance and empty it into the cylinder three times to completely fill the cylinder.
7. If a question in Exercise 20.2 asks for the material needed to build a conical funnel, which surface area should be calculated?
For a conical funnel, you should calculate the Curved Surface Area (CSA = πrl). This is because a funnel is open at both the top and the narrow bottom, and its material only constitutes the slanting surface. The circular base area is not part of the material used.
8. What is the most common mistake students make when using height (h) and slant height (l) in cone formula calculations?
The most common mistake is incorrectly using the slant height (l) in the volume formula. It is critical to remember:
- Volume (V = 1/3πr²h) always uses the perpendicular height (h).
- Surface Area (CSA = πrl) always uses the slant height (l).
