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