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 Blank

What is the volume of the cone in cubic centimeters?

Record your answer to the nearest whole unit. Use 3.14 for π.

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?