How do you find the volume of a cone?
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Transcript of How do you find the volume of a cone?
How do you find the volume of a cone? For example: A cone with height
9cm and radius 2cm
h=9cm
r=2cm
In this lesson you will learn how to develop and apply the formula for volume of a cone
by comparing cones to cylinders.
Let’s ReviewLet’s Review
B
h Cylinder
Volume = Base x heightV = r2h
Let’s ReviewCore Lesson
B = r2
h
Cylinder: V = r2h Cone: V= ???
Let’s ReviewCore Lesson
It takes 3 cones to fill one cylinder with the same radius
and height as the cone
Let’s ReviewCore Lesson
Volume of Cone = Volume of CylinderV = r2h
Let’s ReviewCore Lesson
h=9cm
r=2cm
V = r2h
V = 2 x9cm
V = 123
Let’s ReviewA Common Mistake
V = r2h V = x 6cm
V = cm3
r2hV = 8 cm3
r=2cm
h=6cm
In this lesson you learned how to develop and apply the
formula for volume of a cone by comparing cones to
cylinders.
Let’s ReviewGuided Practice
h=10cm
r=3cm
V = r2h
V = 2 x10cm
V = 303
Find the volume of the cone.
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
Let’s ReviewExtension Activities
Research and explain how the formula for the volume of a cone can be derived without
using calculus.
Let’s ReviewExtension ActivitiesUse 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 =
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.
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