Volume of Cones Lesson 21. 1. Sketch and label a diagram of a cone with a radius of 3 cm and a...
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Transcript of Volume of Cones Lesson 21. 1. Sketch and label a diagram of a cone with a radius of 3 cm and a...
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.
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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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?