1. A conical funnel with a radius of 3 inches and a height of 5 inches is draining liquid at a rate of 2 cubic inches per second. How many seconds will it take to empty, in terms of pi? ___ seconds.
2. A conical water tank has a radius of 2 feet and a height of 9 feet. Water is drained from it at a rate of 0.5 cubic feet per second. It will take ___ seconds to empty the tank, in terms of pi.
3. A conical container is filled with water at a constant rate. If the radius of the cone is doubled, but the height and fill rate remain the same, how does the time to fill the container change?
4. A machine deposits sand into a conical pile with a base diameter of 6 yards and a height of 4 yards. If sand is deposited at 3 cubic yards per hour, how many hours will it take? Express your answer in terms of pi. ___ hours.
5. A machine fills an ice cream cone with a radius of 2.5 cm and a height of 12 cm. If soft-serve is dispensed at a rate of 2.5 cm³/s, how many seconds will it take to fill the cone?
6. A right cone has a radius of 5 meters and a slant height of 13 meters. What is the height of the cone in meters? ___
7. The radius of a cone is 6 cm and its slant height is 10 cm. Find the height of the cone in cm. ___
8. A cone-shaped paper cup has a radius of 15 cm and a slant height of 17 cm. What is the height of the cup in cm? ___
9. A right cone has a radius of 9 feet and a slant height of 41 feet. What is its height?
10. A cone has a slant height of 37 units and a radius of 12 units. Calculate the height of the cone. ___