RD Sharma Class 10 Solutions Chapter 16 - Surface Areas and Volumes (Ex 16.3) Exercise 16.3 - Free PDF
FAQs on RD Sharma Class 10 Solutions Chapter 16 - Exercise 16.3
1. What is the correct step-by-step method to solve problems on the volume of a frustum of a cone in RD Sharma's Exercise 16.3?
To find the volume of a frustum of a cone, follow the method given in RD Sharma solutions:
- Identify the given values: height (h), radius of the upper base (r₁), and radius of the lower base (r₂).
- Use the standard formula for the volume of a frustum: V = (1/3)πh(r₁² + r₂² + r₁r₂).
- Substitute the identified values into the formula.
- Calculate the final result and ensure the units are in cubic units (e.g., cm³ or m³).
2. How do you correctly calculate the total surface area (TSA) of a frustum of a cone for problems in this chapter?
The total surface area of a frustum is the sum of its curved surface area and the areas of its two circular bases. The step-by-step method is:
- First, calculate the slant height (l) using the formula: l = √[h² + (r₁ - r₂)²].
- Next, calculate the curved surface area (CSA): CSA = π(r₁ + r₂)l.
- Calculate the area of the two bases: Area = πr₁² + πr₂².
- Finally, add them all together: TSA = π(r₁ + r₂)l + πr₁² + πr₂². This is the complete method used in the solutions.
3. What is the most common mistake students make when solving frustum problems from RD Sharma Chapter 16?
A common mistake is incorrectly calculating the slant height (l). Students often forget to use the difference of the radii (r₁ - r₂) in the formula l = √[h² + (r₁ - r₂)²] and might just use one radius or add them. Another frequent error is confusing the formula for the total surface area with the curved surface area, leading to an incomplete answer. Always double-check which area is being asked for in the question.
4. Why is calculating the slant height (l) a critical first step for finding surface area but not for volume?
The slant height (l) is crucial for surface area because it represents the length of the slanted surface that you are calculating the area of. The formulas for both Curved Surface Area (π(r₁ + r₂)l) and Total Surface Area depend directly on 'l'. However, the formula for volume, V = (1/3)πh(r₁² + r₂² + r₁r₂), depends on the vertical height (h) of the frustum, not its slanted side. The volume measures the 3D space inside the object, which is defined by its vertical dimension.
5. How do the solutions in RD Sharma for Exercise 16.3 help in solving problems involving the conversion of solids?
The solutions demonstrate a key principle: when one solid is melted and recast into another, their volumes remain equal. For a problem where a cone is cut to form a frustum and a smaller cone, the RD Sharma solutions would guide you to equate the volume of the original large cone to the sum of the volumes of the new frustum and the smaller cone. This approach is fundamental for solving complex combination and conversion problems.
6. What is the step-by-step process for finding the slant height 'l' of a frustum if only the vertical height 'h' and radii 'r₁' and 'r₂' are given?
As per the methods in RD Sharma, finding the slant height is a direct application of the Pythagorean theorem on the cross-section of the frustum. The steps are:
- Identify the vertical height 'h' and the two radii, r₁ and r₂.
- Find the difference between the two radii: (r₁ - r₂).
- Apply the slant height formula: l = √[h² + (r₁ - r₂)²].
- Calculate the square root to find the value of 'l'. This value is then used to find the surface area.
7. How does the concept of a frustum, as explained in RD Sharma, apply to real-world objects?
The frustum of a cone is a very common shape in daily life. The solutions in RD Sharma for Chapter 16 help you calculate the capacity and material required for objects like:
- A bucket used for holding water (volume).
- A glass for drinking (volume/capacity).
- A lampshade (surface area for the material).
- The base of a traffic cone or a funnel.
