1.
a. Find the volume of the cylinder. Write an exact answer in terms of π.
b. Find the volume of a cylinder with the same radius and double the height. Write an exact answer in terms of π.
2. A can of vegetables has a radius 2.3 in. and a height 5.5 in. Find the volume of the can. Use 3.14 for π. Round to the nearest tenth as needed.
3. The volume of a cylinder is 1,029π cm^{3}. The height of the cylinder is 21 cm. What is the radius of the cylinder? Simplify your answer.
4. A company is designing a new cylindrical water bottle. The volume of the bottle will be 103 cm^{3}. The height of the water bottle is 8.1 cm. What is the radius of the water bottle? Use 3.14 for π. Round to the nearest tenth as needed.π
5. You are building a sand castle and want to use a bucket that holds a volume of 885 in.^{3} and has height 11.7 in.
a. What is the radius of the bucket? Use 3.14 for π.
b. If the height of the bucket is changed, but the volume stays the same, then how will the radius change? Explain.
6.
a. Writing Find the volume of a cylinder with radius 10 m and height 8 m. Write an exact answer in terms of π.
b. How does the volume change when the height is tripled? When the radius is tripled? Explain.
7. Error Analysis The cylinder is filled with water. A student was asked to find the volume of water in the cylinder using 3.14 for π. He was asked to decide if the water will fill the rectangular container. He incorrectly said the volume of water in the cylinder is 45.9 in.^{3} and that the water will fill the rectangular container.
a. Find the volume of water in the cylinder. Round to the nearest tenth as needed.
b. Will the water fill the rectangular container?
c. What mistake might the student have made?
8.
a. Find the volume of a cylinder with diameter 8 ft and height 6 ft.
b. Find the volume of the cylinder with the height and radius quadrupled.
c. How many times greater is the volume of the larger cylinder than the smaller cylinder?