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Frustum Concepts - Surface Area & Volume, CBSE Class 10 Mathematics Video Lecture

FAQs on Frustum Concepts - Surface Area & Volume, CBSE Class 10 Mathematics Video Lecture

1. What is a frustum and how is it different from a cone?
Ans. A frustum is a three-dimensional solid that is obtained when a cone is cut by a plane parallel to its base. The frustum has two parallel circular bases and a curved surface connecting them. The main difference between a frustum and a cone is that a frustum has two circular bases of different radii, while a cone has only one circular base.
2. How can we find the surface area of a frustum?
Ans. The surface area of a frustum can be calculated by adding the areas of its curved surface and the areas of its two circular bases. The formula to find the surface area of a frustum is: Surface Area = π(r₁ + r₂)ℓ + πr₁² + πr₂², where r₁ and r₂ are the radii of the two circular bases, and ℓ is the slant height of the frustum.
3. What is the volume of a frustum?
Ans. The volume of a frustum can be calculated using the formula: Volume = (1/3)πh(r₁² + r₂² + r₁r₂), where r₁ and r₂ are the radii of the two circular bases, and h is the height of the frustum.
4. How can we find the height of a frustum if the radii and slant height are given?
Ans. The height of a frustum can be found using the Pythagorean theorem. If the radii of the two circular bases are r₁ and r₂, and the slant height is ℓ, then the height can be calculated as: height = √(ℓ² - (r₂ - r₁)²).
5. Can a frustum have a negative volume or surface area?
Ans. No, a frustum cannot have a negative volume or surface area. Both the volume and surface area of a frustum are always positive values. Negative values do not make sense in the context of the physical dimensions of a frustum.
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