Volume of a cone

Volume of Cones

Lesson # 15

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2019 Open Up Resources |

Let’s explore cones
and their volume.

Today’s Goals

❏ I can find the volume of a cone in mathematical and

real-world situations.

❏ I know the formula for the volume of a cone.

Which Has a Larger Volume?

Warm Up 15.1

Activate: Activity 15.1

● Work quietly

(2-3 min)

● We will have a whole class discussion on #1 and #2

From Cylinders to Cones

Activity 15.2
●

MLR8: Discussion Supports

●

Notice and Wonder

Comprehend/ Apply: Activity 15.2

What do you notice? What do you wonder?

Organize: Activity
15.2 Synthesis

Calculate that Cone

Activity 15.3
●

MLR3: Clarify, Critique, Correct

Comprehend/ Apply: Activity 15.3

I will discuss these problems.

Calculate that Cone

Now it's time for you to practice.

Practice

Drag and Drop

A cylinder has a radius of 4 cm and a height of 12 cm. A cone has the same measurements.



The volume of the cone is ​ ​

Placeholder

times that of the cylinder.

Drag these tiles and drop them in the correct blank above

2

3

Multiple Choice

Which 3-dimensional figure is associated with the volume formula, $$V=\frac{1}{3}\pi r^2h$$ ?

• pyramid

• cylinder

• sphere

• cone

Multiple Choice

Which equation represents the volume of the cone shown in cubic centimeters?

• $$V\ =\ 80\ \times150\ \times\pi$$

• $$V\ =\frac{1}{3}\times\pi\times80^2\times150$$

• $$V\ =\frac{1}{2}\times\pi\times80^2\times170$$

• $$V\ =\ 80\ \times150\ \times170\times\pi$$

Fill in the Blanks

Multiple Choice

Which is closest to the volume of Mike's cup?

• 21 cubic inches

• 63 cubic inches

• 66 cubic inches

• 198 cubic inches

Multiple Choice

What is the volume, in cubic inches, of the cone?

• 18π

• 27π

• 81π

• 108π

Organize: Lesson 15 Synthesis

●What is the relationship between the volume of a cylinder and the volume
of a cone?

●If we know the volume of a cone, how do we calculate the volume of a
cylinder that has the same height and base area?

●If we know the volume of a cylinder, how do we calculate the volume of a
cone that has the same height and base area?

●If a cylinder and a cone have the same base, how tall does the cone have
to be relative to the cylinder so that they both have the same volume?

Today’s Goals

❏ I can find the volume of a cone in mathematical and

real-world situations.

❏ I know the formula for the volume of a cone.

Calculate Volume of Two Figures

Cool Down 15.4

Apply/ Summarize: Activity 15.4

Need a challenge?