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Volume of Cones
1
October 10, 2014
Objective: I will be able to calculate the volume of a cone using the formula.
Warm Up:Find the volume of the following cylinders
Radius: 2'' Height: 4''
Radius: 5cm Height: 28 cm
Radius: 4' Height: 25'
Radius: 5.6'' Height: 10''
Volume of Cones
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October 10, 2014
We Do: Rapid Review
What is volume?
How do we measure it? Is there a "general" formula for finding volume?
Yes, base (length times width) times height!
Volume of Cones
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October 10, 2014
Think. What is a cone?
Volume of Cones
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October 10, 2014
I Do: Vocabulary
A cone is a threedimensional figure with a circular base connected by a curved surface to a single vortex.
Volume of Cones
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October 10, 2014
Draw a "Double Bubble Map" Comparing Cones and Cyllinders
Think. We already know the volume of a cone. How are cylinders and cones similar?
Volume of Cones
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October 10, 2014
Proving the formula!
http://www.youtube.com/watch?v=QnVr_x7c79w
Volume of Cones
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October 10, 2014
I Do: Finding the Volume of a Cone
Remember: Volume=1/3πr2h
If a cone had a height of 10ft and a radius of 5 feet, what would the volume be?
The volume of a cone is 471.24 cubic inches and the height is 8 inches. What is the radius of the cone?
Volume of Cones
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October 10, 2014
We Do: Finding the Volume of a Cone
Remember: Volume=1/3πr2h
If a cone had a height of 9.2 inches and a radius of 3 inches, what would the volume be?
Volume of Cones
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October 10, 2014
You Do: Finding the Volume of a Cone
Remember: Volume=1/3πr2h
If a cone had a height of 3 yards and a radius of 4 yards, what would the volume be?
Volume of Cones
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October 10, 2014
You Do: Find the volume of the following cones. When you are done, check your work with your shoulder partner.
Volume of Cones
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October 10, 2014
You Do:
A party hat is going to be filled with candy. If it has a height of 8 inches and a radius of 7 inches. How many cubic inches of candy could it hold?
The Colorado Department of Transportation stores road salt in conical buildings. If the building has a diameter of 4 meters and a height of 3.8 meters, how many cubic meters of salt can it hold? Suppose the CDT wants to store 10,000 cubic meters of salt, how many buildings would they need?
Volume of Cones
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October 10, 2014
You Do:
A cylinder has a radius of 5 centimeters and a height of 12 centimeters. What would the height of the cone need to be to have the same volume if the radius was the same?
The volume of a cone with a 30mm radius is 9,420 cubic mm. What is the height of the cone?
Volume of Cones
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October 10, 2014
You Do: Find the ErrorCarmen is finding the volume of rice that will fill a coneshaped vase. The vase is 6 inches tall with a diameter of 4 inches.
Carmen decides that: Volume=1/3π x 4 x 4 x 6 Volume=100.5 cubic inches
Find her mistake and correct it! Explain your thinking
Volume of Cones
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October 10, 2014
You Do: Extension
Think. What would have the greater effect on the volume of a cone: doubling its radius or doubling its height? Why? Prove your idea by completing an example with real numbers.
Volume of Cones
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October 10, 2014
DOL: Find the volume of the figure below. Round to the nearest tenth. Do not leave in terms of pi.