Grade 12 Math: Frustums
This worksheet focuses on understanding and calculating properties of frustums, including surface area and volume, suitable for Grade 12 Geometry students.
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Grade 12 Math: Frustums
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Read each question carefully and provide detailed solutions. Show all your work for full credit. Use π ≈ 3.14 where necessary.
1. Define a frustum of a cone and describe its key geometric properties.
2. Which of the following formulas represents the volume of a frustum of a cone?
V = (1/3)πh(R² + r²)
V = (1/3)πh(R² + Rr + r²)
V = (1/3)πh(R - r)²
V = (1/3)πh(R + r)²
3. A frustum of a cone has a height of 10 cm. The radii of its circular bases are 8 cm and 4 cm. Calculate the volume of the frustum.
4. The lateral surface area of a frustum of a cone is given by the formula L = πl(R + r), where l is the .
5. A frustum can be formed by cutting off the of a cone with a plane parallel to its base.
6. A frustum of a square pyramid has a height of 12 cm. The side lengths of its square bases are 10 cm and 6 cm. Calculate the total surface area of the frustum.
7. The slant height of a frustum of a cone is always greater than its height.
True
False
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