Concept Byte: Finding Volume

Use With Lesson 11-5

ACTIVITY

You know how to find the volumes of a prism and of a cylinder. Use the following activities to explore finding the volumes of a pyramid and of a cone.

Activity 1

• Step 1 Draw the nets shown below on heavy paper.

• Step 2 Cut out the nets and tape them together to make a cube and a square pyramid. Each model will have one open face.

1. How do the areas of the bases of the cube and the pyramid compare?
2. How do the heights of the cube and the pyramid compare?
3. Fill the pyramid with rice or other material. Then pour the rice from the pyramid into the cube. How many pyramids full of rice does the cube hold?
4. The volume of the pyramid is what fractional part of the volume of the cube?
5. Make a Conjecture What do you think is the formula for the volume of a pyramid? Explain.

Activity 2

• Step 1 Draw the nets shown below on heavy paper.

• Step 2 Cut out the nets and tape them together to make a cylinder and a cone. Each model will have one open face.

6. How do the areas of the bases of the cylinder and of the cone compare?
7. How do the heights of the cylinder and of the cone compare?
8. Fill the cone with rice or other material. Then pour the rice from the cone into the cylinder. How many cones full of rice does the cylinder hold?
9. What fractional part of the volume of the cylinder is the volume of the cone?
10. Make a Conjecture What do you think is the formula for the volume of a cone? Explain.

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