Volume and Surface Area of Cones
Calculate the volume and surface area of various cones, applying formulas and understanding geometric properties.
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Volume and Surface Area of Cones
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Read each question carefully and calculate the volume and surface area of the cones as indicated. Use π ≈ 3.14 and round your answers to two decimal places where necessary.
1. A cone has a radius of 5 cm and a height of 12 cm. Calculate its volume.
2. Find the volume of a cone with a diameter of 10 meters and a slant height of 13 meters.
3. Calculate the lateral surface area of a cone with a radius of 7 cm and a slant height of 10 cm.
4. A cone has a radius of 6 feet and a height of 8 feet. Find its total surface area.
5. Which of the following formulas represents the volume of a cone?
V = πr²h
V = (1/3)πr²h
V = 2πrh
V = πr(r + l)
6. The formula for the total surface area of a cone is:
SA = πrl
SA = πr² + 2πrh
SA = πr² + πrl
SA = (1/3)πr²h
7. The slant height of a cone can be found using the Pythagorean theorem if the radius and are known.
8. The base of a cone is a .
9. To find the total surface area of a cone, you add the area of the base to the surface area.
10. Doubling the radius of a cone will double its volume.
True
False