unit volume homework 3 applying volume of cylinders and cones

Volumes of Cones and Cylinders

Examples, videos, and solutions to help Grade 8 students learn the volume formulas for cones and cylinders.

New York State Common Core Math Grade 8, Module 5, Lesson 10

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Volume Activities and 7 Teaching Tips

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Volume is one of my favorite middle school math skills to teach. The skill is visual and concrete, requires sketching pictures (which is always fun to tease what a great artist I am), and the operations required for solving allow for spiraled practice. A real winner from this teacher’s point of view!

Here are my 7 tips/ideas for teaching volume in a way that students will get the most from it.

Start with Area

While most scope and sequences require mastering area (or surface area) before moving onto volume, the connection between area and volume cannot be ignored.

In fact, in all of the formulas for volume, the area of the base is abbreviated as ‘B’. And while this formula chart does give the formula for the various shapes’ areas, it does that separate from the volume formulas. 

Encourage students to shade the base in every problem and then sketch the base separately with its dimensions. This helps students to actually calculate the area of the base instead of  using only one of it’s measurements, which was often the most common misconception I witnessed. 

This Desmos Activity really helps make the connection between the area of the base and the height.

Write down the Formula + Draw the Shape

You don’t have to provide formulas when you first introduce volume! Have students make observations and predictions. For example, using a rectangular prism and a triangular prism with the same height and base measurements, ask – “how many triangular prisms could fit inside the rectangular prism?” You can do this for a cone and a cylinder too! Unifix cubes are the perfect manipulatives to use for students to understand how volume is measured in a rectangular prism. 

After you have introduced the formula for a shape, require students to write down the formula for the shape as part of their work. This will prevent students from leaving off multiplying by ⅓ for the volume of a cone or 4/3 for a sphere. I would even make this mistake on purpose, so students would shoot up their hands and say, “Ms. Brack, you forgot to multiply by ⅓!”

In addition, if a given problem lacked a figure, I required students to draw the figure and label the sides with the given measurements. 

Use the Exact Formula Chart They Will See on Testing Day

Set your students up for success for testing day! Provide students with the EXACT formula chart they will see when they take their state test. I made a class set on bright neon cardstock that I would laminate. It stayed out throughout the entirety of my Geometry Unit. 

During a geometry lesson,  I would always instruct my students to silently point to the formula we would need on their formula chart.  I would do a quick sweep to make sure students were on the right track. Don’t assume your students will understand how to find what they need from a formula chart. 

Start with an Exploratory Activity

This is pretty obvious, but volume is so hands-on! It is physically all around us. 

You can do this in a variety of ways: calculating the volume of various items like – tissue boxes, cereal boxes, oatmeal canisters, saltine boxes etc. A sleeve of crackers is the perfect cylinder and is a perfect way to show how the volume is the area of the base times height.

Our Exploration Activity helps students explore the relationships between cylinders and cones using play dough or dried beans. You can find it in our 8th grade volume activity bundle .

This is a free activity that sounds like a perfect way to include a project for rectangular prisms. Students are given a single piece of paper and instructed to create the largest possible box. 

Maneuvering the Middle Activities

Our activity bundles are engaging and hands on! With all of the shapes that are covered in middle school math, it’s nice to know that every prism, cylinder, cone, and sphere will receive practice.

• 6th Grade Geometry Activity Bundle
• 7th Grade Volume Activity Bundle
• 8th Grade Volume Activity Bundle

Use fabric measuring tapes over rulers. They are less expensive, take up less space, and students will not be tempted to sword fight. 

If you have access to unifix cubes , give students a specific volume and have them work backwards to create as many rectangular prisms with different measurements that satisfies that volume. 

What tips do you have for teaching volume?

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• → 8th Grade

Volume of Cylinders, Cones, and Spheres Lesson Plan

Get the lesson materials.

Volume of Cylinders, Cones, and Spheres Guided Notes

Ever wondered how to teach volume calculations of cylinders, cones and spheres in an engaging way to your 8th grade students? In this lesson plan, students will learn about volume calculations and their real-life applications.

Through artistic, interactive guided notes, check for understanding, maze, doodle & color by number activities, and real-life application of paint in a can, students will gain a comprehensive understanding of volume calculations.

The lesson culminates with a real life example that explores how the volume calculation is used in measuring paint in a can.

• Type : Lesson Plans
• Grade : 8th Grade
• Standard : CCSS 8.G.C.9

Learning Objectives

After this lesson, students will be able to:

Know the formulas for the volume of cylinders, cones, and spheres

Calculate the volume of cylinders, cones, and spheres

Apply the concept of volume to real-life situations, such as measuring the volume of paint in a can.

Prerequisites

Before this lesson, students should be familiar with:

Basic multiplication and division skills

How to evaluate exponents (powers of 2 and 3)

Basic understanding of fractions and decimals (optional, but helpful)

Colored pencils or markers

Volume of Cylinders, Cones, & Spheres

Guided Notes

Key Vocabulary

Cubic Units

Introduction

As a hook, ask students why it is important to be able to calculate the volume of objects like cylinders, cones, and spheres. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the guided notes to introduce the concept of finding volume of cylinders, cones, and spheres. Walk through the key points of the topic of the guided notes to teach. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Have students walk through the “Volume Practice” section. Call on students to talk through their answers, potentially on the whiteboard or projector. Based on student responses, reteach concepts that students need extra help with.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

Have students practice finding the volume of cylinders, cones, and spheres using the Doodle Math activity. Walk around to answer student questions.

Fast finishers can dive into the maze for extra practice. You can assign it as homework for the remainder of the class.

Real-Life Application

Bring the class back together, and introduce the concept of measuring the volume of paint in a can. Explain how understanding the volume of the can and the amount of paint inside can help determine how much paint is needed for a project, and how it can save time and money by avoiding over-purchasing paint.

Refer to the FAQs below for more ideas on how to teach this real-life application.

Additional self-checking digital practice

If you’re looking for digital practice for volume calculations of cylinders, cones, and spheres, try the Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun and a powerful tool for differentiation.

Volume of Cylinders, Cones, and Spheres 3 Pixel Art

Additional print practice

A fun, no-prep way to practice volume calculations of cylinders, cones, and spheres is Doodle & Color by Number — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Volume of Cylinders, Cones, & Spheres Doodle & Color by Number

What is the formula for finding the volume of a cylinder? Open

The formula for finding the volume of a cylinder is pi times the radius squared times the height of the cylinder.

What is the formula for finding the volume of a cone? Open

The formula for finding the volume of a cone is one-third times pi times the radius squared times the height of the cone.

What is the formula for finding the volume of a sphere? Open

The formula for finding the volume of a sphere is four-thirds times pi times the radius cubed.

Why is it important to know how to calculate the volume of objects like cylinders, cones, and spheres? Open

Knowing how to calculate the volume of objects like cylinders, cones, and spheres is important in many real-life situations, such as measuring the volume of paint in a can or calculating the volume of objects such as traffic cones, and even megaphones.

What are cubic units? Open

Cubic units are units of measurement used to measure the volume of objects in three-dimensional space.

What is an exponent? Open

An exponent is a mathematical notation that indicates the number of times a quantity is multiplied by itself.

Want more ideas and freebies?

Get my free resource library with digital & print activities—plus tips over email.

Volume of Cylinders, Cones and Spheres Unit Review Activity

Also included in

Description

This Volume of Cylinders, Cones and Spheres Cut and Paste is a great way to practice solving problems involving the volume of cylinders, cones and spheres. Students will match the cylinder, cone or sphere to the correct formula and total volume.

This activity is great for extra practice, as a station or center, and can be used to add variety to homework or independent work. Students can be hands-on, while still applying their understanding of volume of cylinders, cones and spheres.

Students are able to practice and apply concepts with this volume activity, while collaborating and having fun! Math can be fun and interactive!

Standards: CCSS (8.G.9) and TEKS (8.7A)

More details on what is included:

30 ready-to-print formula and volume cards that can be utilized in pairs or groups of 3-4 and any necessary recording sheets and answer keys.

• Cut and Paste: Volume of Cylinders, Cones and Spheres
• Recording Sheet
• Teacher Directions

***Please download a preview to see sample pages and more information.***

How to use this resource:

• Use as a whole group classroom activity
• Use in a small group for additional remediation, tutoring, or enrichment
• Use as an alternative homework or independent practice assignment
• Incorporate within our Volume Unit to support the mastery of concepts and skills.

Time to Complete:

• Most activities can be utilized within one class period. Performance tasks summarize the entire unit and may need 2-3 class periods. However, feel free to review the activities and select specific problems to meet your students’ needs and time specifications. There are multiple problems to practice the same concepts, so you can adjust as needed.

Looking for instructional materials? 

• Check out the corresponding Volume Unit , which includes student handouts, independent practice, assessments, and answer keys.

More 8th Grade Activity Bundles:

Unit 1: Real Number System 

Unit 2: Exponents and Scientific Notation

Unit 3: Linear Equations

Unit 4: Linear Relationships

Unit 5: Functions

Unit 6: Systems of Equations

Unit 7: Transformations

Unit 8: Angle Relationships

Unit 9: Pythagorean Theorem

Unit 10: Volume Unit 11: Scatter Plots and Data

More 8th Grade Units:

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