How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm...
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Transcript of How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm...
![Page 1: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/1.jpg)
How do you find the volume of a cone? For example: A cone with height
9cm and radius 2cm
h=9cm
r=2cm
![Page 2: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/2.jpg)
In this lesson you will learn how to develop and apply the formula for volume of a cone
by comparing cones to cylinders.
![Page 3: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/3.jpg)
Let’s ReviewLet’s Review
B
h
Cylinder
Volume = Base x height
V = r2h
![Page 4: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/4.jpg)
Let’s ReviewCore Lesson
B = r2
h
Cylinder: V = r2h
Cone: V= ???
![Page 5: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/5.jpg)
Let’s ReviewCore Lesson
It takes 3 cones to fill one cylinder with the same radius
and height as the cone
![Page 6: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/6.jpg)
Let’s ReviewCore Lesson
Volume of Cone = Volume of Cylinder
V = r2h
![Page 7: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/7.jpg)
Let’s ReviewCore Lesson
h=9cm
r=2cm
V = r2h
V = 2 x9cm
V = 123
![Page 8: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/8.jpg)
Let’s ReviewA Common Mistake
V = r2h
V = x 6cm
V = cm3
r2h
V = 8 cm3
r=2cm
h=6cm
![Page 9: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/9.jpg)
In this lesson you learned how to develop and apply the
formula for volume of a cone by comparing cones to
cylinders.
![Page 10: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/10.jpg)
Let’s ReviewGuided Practice
h=10cm
r=3cm
V = r2h
V = 2 x10cm
V = 303
Find the volume of the cone.
![Page 11: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/11.jpg)
Let’s ReviewGuided Practice
Find the volume of the cone.
d=8cm
h=12cm
V = r2h
V = 2x 12cm
V = 64 cm3
d=8cm so
r=4cm
![Page 12: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/12.jpg)
Let’s ReviewExtension Activities
Research and explain how the formula for the volume of a cone can be derived without
using calculus.
![Page 13: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/13.jpg)
Let’s ReviewExtension Activities
Use measurement and geometrical shapes to demonstrate the relationship between
the volume of a cone and volume of a similar cylinder.
Record your measurements and calculate the percent error in your measurements
assuming the actual relationship is
Vcone =
![Page 14: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/14.jpg)
Let’s ReviewExtension Activities
Demonstrate, using cones and cylinders with similar dimensions, that the volume of a cone is one-third the
volume of a cylinder.
![Page 15: How do you find the volume of a cone? For example: A cone with height 9cm and radius 2cm h=9cm r=2cm.](https://reader030.fdocuments.us/reader030/viewer/2022032723/56649f565503460f94c79c10/html5/thumbnails/15.jpg)
Let’s ReviewQuick Quiz
1. Find the volume of a con with height 15cm and radius 5cm
2. Find the volume of a cone with height 10cm and radius 3cm