Volume of Cones

Lesson 21

1. Sketch and label a diagram of a cone with a radius of 3 cm and a height of 7 cm.

2. Find the surface area of the cone in #1.

3. A cone and a cylinder have congruent bases and are the same height. Predict what the relationship between their volumes will be.

Target: Calculate the volume of cones.

The volume of a cone is equal to one-third of the product of the area of the base (B) and the height (h).

3Vor

3

1V

BhBh

3Vor h

3

1V

22 hrr

Find the volume of the cone. Use 3.14 for π.

Write the formula. V = πr2h

Substitute known values. V ≈ (3.14)(4)2(12)

Find the value of the power. V ≈ (3.14)(16)(12)

Multiply. V ≈ 200.96

The volume of the cone is about 200.96 cm3.

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3

1

3

1

Chantel helped with her sister’s party. Each child received aparty hat full of treats. Each hat had a volume of 65.94 cubicinches. The radius of each hat was 3 inches. How tall waseach party hat?

Write the formula. V = πr2h Substitute known values. 65.94 ≈ (3.14)(3)2h

Find the value of the power. 65.94 ≈ (3.14)(9)h

Multiply. 65.94 ≈ 9.42h Divide by 9.42 on both sides. 9.42 9.42

7 ≈ h Each party hat was about 7 inches tall.

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1. Find the volume of the cone. Use 3.14 for .

2. A cone has a volume of 30 cubic inches. What is the volume of a cylinder with the same height and a congruent base to the cone?

What is similar about cones and pyramids? What is different?