Grade 12 Math: Volume and Surface Area of Cones
A worksheet for Grade 12 students covering the calculation of volume and surface area of cones, including real-world applications.
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Grade 12 Math: Volume and Surface Area of Cones
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Read each question carefully and show all your work. Use π ≈ 3.14 for calculations unless otherwise specified. Round your answers to two decimal places where necessary.
1. A cone has a radius of 7 cm and a height of 12 cm. Calculate its volume.
2. The volume of a cone is 300π cubic meters. If its height is 9 meters, find its radius.
3. A cone has a radius of 5 cm and a slant height of 13 cm. Calculate its total surface area.
4. Find the lateral surface area of a cone with a diameter of 10 inches and a slant height of 15 inches.
5. Which of the following formulas represents the volume of a cone?
V = πr²h
V = (1/3)πr²h
V = 2πrh
V = πrl
6. If the height of a cone is doubled while its radius remains constant, how does its volume change?
It doubles
It quadruples
It halves
It remains the same
7. The formula for the lateral surface area of a cone is .
8. The is the distance from the apex of a cone to any point on the circumference of its base.
9. If a cone and a cylinder have the same base area and height, the volume of the cone is one-third the volume of the cylinder.
True
False
10. The total surface area of a cone includes the area of its base and its lateral surface area.
True
False
11. An ice cream cone has a height of 10 cm and a diameter of 6 cm. If the cone is completely filled with ice cream, what is the volume of ice cream it holds? (Ignore the top scoop of ice cream, just the cone portion).
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