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![Page 1: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/1.jpg)
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''
![Page 2: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/2.jpg)
Volume of Cones
2
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!
![Page 3: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/3.jpg)
Volume of Cones
3
October 10, 2014
Think. What is a cone?
![Page 4: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/4.jpg)
Volume of Cones
4
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.
![Page 5: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/5.jpg)
Volume of Cones
5
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?
![Page 6: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/6.jpg)
Volume of Cones
6
October 10, 2014
Proving the formula!
http://www.youtube.com/watch?v=QnVr_x7c79w
![Page 7: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/7.jpg)
Volume of Cones
7
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?
![Page 8: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/8.jpg)
Volume of Cones
8
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?
![Page 9: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/9.jpg)
Volume of Cones
9
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?
![Page 10: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/10.jpg)
Volume of Cones
10
October 10, 2014
You Do: Find the volume of the following cones. When you are done, check your work with your shoulder partner.
![Page 11: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/11.jpg)
Volume of Cones
11
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?
![Page 12: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/12.jpg)
Volume of Cones
12
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?
![Page 13: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/13.jpg)
Volume of Cones
13
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
![Page 14: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/14.jpg)
Volume of Cones
14
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.
![Page 15: Volume of Cones - Weeblycarmel8math.weebly.com/uploads/4/0/7/1/40717803/volume_of_con… · Volume of Cones 12 October 10, 2014 You Do: A cylinder has a radius of 5 centimeters and](https://reader036.vdocument.in/reader036/viewer/2022062411/6023615c08e9c42575312b05/html5/thumbnails/15.jpg)
Volume of Cones
15
October 10, 2014
DOL: Find the volume of the figure below. Round to the nearest tenth. Do not leave in terms of pi.