Lesson 14 Classwork

The volume V of a cylinder with radius r is given by the formula V=πr2h.

1. The volume of this cylinder with radius 5 units is 50π cubic units. This statement is true:50π=52πhWhat does the height of this cylinder have to be? Explain how you know.
2. The volume of this cylinder with height 4 units is 36π cubic units. This statement is true:36π=r2π4What does the radius of this cylinder have to be? Explain how you know.

"Are you ready for more?"Suppose a cylinder has a volume of 36π cubic inches, but it is not the same cylinder as the one you found earlier in this activity.

1. What are some possibilities for the dimensions of the cylinder?
2. How many different cylinders can you find that have a volume of 36πcubic inches?

Student-Facing Task StatementThis cylinder has a volume of 12π cubic inches and a diameter of 4 inches. Find the cylinder's radius and height.