Navigation

6-8 Accelerated 7 Unit 6 Lesson 15

Gradeband

K-5 Math •6-8 Math 9-12 Math

Course

Accelerated 6 •Accelerated 7

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 •Unit 6 Unit 7 Unit 8 Unit 9

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 •Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22 Lesson 23

K-5
6-8
9-12

Accelerated 6
Accelerated 7

Grade 6
Grade 7
Grade 8

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18
Lesson 19
Lesson 20
Lesson 21
Lesson 22
Lesson 23

Lesson | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

IM® 6-8 Math v.360, an IM v.360 curriculum, is ©2024 by Illustrative Mathematics®, and licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

IM 6-8 Math v.360, an IM v.360 curriculum, is a derivative of IM 6-8 Math.

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics®, and is ©2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) . OUR's 6-8 Math Curriculum is available at https://openupresources.org/math-curriculum/ .

Adaptations and updates to IM 6-8 Math v.360 are ©2024 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution-Noncommercial 4.0 International License (CC BY-NC 4.0).

Adaptations and additions to create IM 6–8 Math v.360 Accelerated are ©2025 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY-NC 4.0).

Adaptations to add additional English language learner supports are ©2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The second set of English assessments (marked as set “B”) are ©2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) .

Spanish translation of the “B” assessments are ©2020 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Settings

Audience

family

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Lesson 15

15.1 Warm-up 15.2 Activity 15.3 Activity Student Lesson Summary

Unit 6, Lesson 15

The Volume of a Cone

Accelerated 7

15.1

Warm-up

Which Has a Larger Volume?

The cone and cylinder have the same height, and the radii of their bases are equal.

Which figure has a larger volume?
Do you think the volume of the cone is more or less than the volume of the cylinder? Explain your reasoning.
Sketch two different sized cones. The oval doesn’t have to be on the bottom!
For each drawing, label the cone’s radius with and height with .
Here is a method for quickly sketching a cone:
- Draw an oval.
- Draw a point centered above the oval.
- Connect the edges of the oval to the point.
- Which parts of your drawing would be hidden behind the object? Make these parts dashed lines.

Are You Ready for More?

15.2

Activity

From Cylinders to Cones

A cone and cylinder have the same height, and their bases are congruent circles.

A right circular cylinder and a right circular cone. Both the cylinder and the cone have a height labeled h and have a radius labeled r.

If the volume of the cylinder is 90 cm³, what is the volume of the cone?
If the volume of the cone is 120 cm³, what is the volume of the cylinder?
If the volume of the cylinder is , what is the volume of the cone? Either write an expression for the cone or explain the relationship in words.

Are You Ready for More?

15.3

Activity

Calculate That Cone

Here is a cylinder and cone that have the same height and the same base area.

What is the volume of each figure? Express your answers in terms of .
Here is a cone.
1. What is the area of the base? Express your answer in terms of .
2. What is the volume of the cone? Express your answer in terms of .
A cone-shaped popcorn cup has a radius of 5 centimeters and a height of 9 centimeters. How many cubic centimeters of popcorn can the cup hold? Use 3.14 as an approximation for , and give a numerical answer.

Are You Ready for More?

Student Lesson Summary

If a cone and a cylinder have the same base and the same height, then the volume of the cone is of the volume of the cylinder.

For example, the cylinder and cone shown here both have a height of 7 feet and a base with radius 3 feet.

The cylinder has a volume of cubic feet since .

The cone has a volume that is of that, or cubic feet.

An image of a right circular cone and a right circular cylinder. The cone has a height of 7 and radius of 3. The cylinder has a height of 7 and a radius of 3.

If the radius for both solids is and the height for both solids is , then the volume of the cylinder is . That means that the equation to give the volume, , of the cone is

Glossary

None