1. What is the exact volume of the figure? Write an exact answer in terms of π.
2. Order the cones described below from least to greatest volume.
Cone 1: radius 6 cm and height 12 cm
Cone 2: radius 12 cm and height 6 cm
Cone 3: radius 9 cm and height 8 cm
3. How many cubic meters of material are there in a conical pile of dirt that has radius 11 meters and height 6 meters? Use 3.14 for π. Round to the nearest hundredth as needed.
4. Think About the Process
a. What is the radius of a cone with diameter d?
A. The radius is d.
B. The radius is d over 2 .
C. The radius is 2d.
D. There is not enough information to find the radius of the cone.
b. An ice cream cone is filled exactly level with the top of the cone. The cone has a 9-cm diameter and 9-cm depth. Approximately how much ice cream (in cm^{3}) is in the cone? Use 3.14 for π. Round to the nearest hundredth as needed.
5. A special stainless steel cone sits on top of a cable television antenna. The cost of the stainless steel is $8.00 per cubic centimeter. The cone has radius 12 cm and height 10 cm. What is the cost of the stainless steel needed to make this solid steel cone? Use 3.14 for π. Round to the nearest cent as needed.
6. The volume of the cone is 147π yd^{3}. What is the radius of the cone?
7. An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 7 feet tall and has total volume 109.9 cubic feet, what is the radius of the sculpture? Use 3.14 for π. Round to the nearest tenth as needed.
8. The volume of a cone-shaped hole is 49π ft^{3}. If the hole is 3 ft deep, what is the radius of the hole?
9. Think About the Process
a. What might be a good first step when solving the equation v equals , 1 third , pi , r squared , h for r? Select all that apply.
A. Divide each side of the equation by 3.
B. Multiply each side of the equation by 3.
C. Divide each side of the equation by h.
D. Multiply each side of the equation by h.
b. A prop for a movie is a cone with height 36 yd and volume 56 , and 1 third , pi , yd cubed . Find the radius of the cone. Round to the nearest hundredth as needed.
10.
a. Writing Find the exact volume of the cone. Write an exact answer in terms of π.
b. Explain why an answer in terms of π is more accurate than an answer that uses 3.14 for π.
11.
a. Reasoning A cone with radius 3 and height 11 has its radius quadrupled. How many times greater is the volume of the larger cone than the smaller cone?
b. Explain how the volume of the cone would change if the radius were divided by four.