Grade 11 Math Worksheet: Frustums
Explore the properties and calculations of frustums, including volume and surface area, with this Grade 11 math worksheet.
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Grade 11 Math Worksheet: Frustums
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Read each question carefully and answer to the best of your ability. Show all your work for calculations.
A frustum is a portion of a solid, normally a cone or pyramid, that lies between two parallel planes cutting the solid. Let's explore its properties.
1. Which of the following best describes a frustum?
A solid with only one circular base.
A cone with its top cut off by a plane perpendicular to its axis.
A pyramid with a square base.
A cylinder without a top base.
2. The volume of a frustum of a cone is found by subtracting the volume of the smaller cone from the volume of the larger cone. True or False?
True
False
3. A frustum of a pyramid is formed when a pyramid is cut by a plane parallel to its base, resulting in two bases.
4. The lateral surface area of a frustum of a cone is given by the formula A = π(R + r)l, where R and r are the radii of the two bases and l is the height.
5. A frustum of a cone has a top radius of 3 cm, a bottom radius of 6 cm, and a height of 4 cm. Calculate its volume. (Use π = 3.14)
6. Explain the difference between a frustum of a cone and a complete cone.
Match the term with its definition.
7. Frustum
a. The distance between the two bases of a frustum.
8. Slant height
b. A portion of a solid cut by two parallel planes.
9. Height
c. The diagonal distance on the lateral surface of a frustum.
10. A lampshade is in the shape of a frustum of a cone. The top diameter is 20 cm, the bottom diameter is 30 cm, and the slant height is 13 cm. Calculate the lateral surface area of the lampshade. (Leave your answer in terms of π)