Lesson 21

Cylinders, Cones, and Spheres

Let’s find the volume of shapes.

Problem 1

A scoop of ice cream has a 3-inch diameter. How tall should the ice cream cone of the same diameter be in order to contain all of the ice cream inside the cone?

Problem 2

Calculate the volume of the following shapes with the given information. For the first three questions, give each answer both in terms of \(\pi\) and by using \(3.14\) to approximate \(\pi\). Make sure to include units.

  1. Sphere with a diameter of 6 inches

  2. Cylinder with a height of 6 inches and a diameter of 6 inches

  3. Cone with a height of 6 inches and a radius of 3 inches

  4. How are these three volumes related?

Problem 3

A coin-operated bouncy ball dispenser has a large glass sphere that holds many spherical balls. The large glass sphere has a radius of 9 inches. Each bouncy ball has radius of 1 inch and sits inside the dispenser.

If there are 243 bouncy balls in the large glass sphere, what proportion of the large glass sphere’s volume is taken up by bouncy balls? Explain how you know.


Problem 4

A farmer has a water tank for cows in the shape of a cylinder with radius of 7 ft and a height of 3 ft. The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity. What is the volume of the tank be when the sensor turns on?

(From Unit 5, Lesson 13.)