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Volume of Cylinders, Cones & Spheres

Eighth graders find the volume of cylinders, cones, and spheres using π — discovering the beautiful relationships between them, like a cone being exactly one-third of a cylinder.

Grade 8Volume50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Find the volume of a cylinder.
  • ✓Find the volume of a cone.
  • ✓Find the volume of a sphere.
  • ✓See how the formulas relate.
Essential Question

A can, an ice-cream cone, and a ball — all round 3-D shapes. How much space does each hold, and how are their volume formulas connected?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Volume Explorer

Project this and switch between a cylinder, cone, and sphere. Change the radius and height, and watch the volume formula work!

🧊 Explore the volume of round 3-D shapesTry it
Radius: 3
Height: 6

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Round Shapes

5 min

A can, a cone, and a ball — how much does each hold?

👩‍🏫 Teacher Moves

  • Show the three shapes.
  • Ask about their volumes.
  • Set the goal: volume.

🎒 Student Actions

  • See the shapes.
  • Wonder the volume.
  • Predict the idea.
2

I Do — The Formulas

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Cylinder: πr²h.
  • Cone: ⅓ of that.
  • Sphere: ⁴⁄₃πr³.

🎒 Student Actions

  • Learn cylinder.
  • Learn cone.
  • Learn sphere.
3

We Do — Explore Together

13 min

Class uses the Volume Explorer.

👩‍🏫 Teacher Moves

  • Switch shapes.
  • Change radius and height.
  • Read the volume.

🎒 Student Actions

  • Switch shapes.
  • Set values.
  • Read volume.
4

You Do — On Your Own

12 min

Students find volume.

👩‍🏫 Teacher Moves

  • Find cylinder volumes.
  • Find cone and sphere volumes.
  • Use π ≈ 3.14.

🎒 Student Actions

  • Find volumes.
  • Use the formulas.
  • Use π.
5

Close — Close

5 min

One shape.

👩‍🏫 Teacher Moves

  • Give a shape with measurements.
  • Find its volume.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find the volume.
  • Explain it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
8.G.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them.

CCSS
8.G.9

Solve real-world problems involving volume.

CCSS
8.G

Understand and apply geometric measurement.

SMP
MP.4

Model 3-D objects with volume formulas.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Formula reference cards.
  • Sentence frame: “Volume = ___ ≈ ___.”
  • Fill shapes to compare.

Support & Access

IEP / 504
  • Start with cylinders.
  • Provide the formula.
  • Use π ≈ 3.14.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Solve composite-solid volumes.
  • Compare cone and cylinder.
  • Find a missing dimension.
Materials

What to gather

  • 📽️Projector / board
  • 🧊3-D shape models
  • 💻The Volume Explorer
  • 🧮Calculators
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

volumethe space inside a 3-D shapecylindera shape with two circular basesconea shape with one circular base and a pointspherea perfectly round ballradiusfrom the center to the edgepi (π)≈ 3.14cubic unitsthe units for volumeformulaa rule for calculating
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What is the volume of a cylinder with radius 3 and height 4? (π ≈ 3.14)
About 113.0 cubic units (3.14 × 9 × 4).
QUESTION 2
How does a cone’s volume compare to a cylinder with the same radius and height?
The cone is exactly one-third of the cylinder.
QUESTION 3
What measurement does a sphere’s volume depend on?
Only its radius.

Going deeper? Composite solids.

Have students find the volume of a composite shape, like a cylinder topped with a cone (an ice-cream cone!). A printable volume sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Volume of Cylinders, Cones & SpheresFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Volume of Cylinders, Cones & SpheresQuiz
Score: 0
1 / 6
Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Volume of Cylinders, Cones & SpheresPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: cone, cubic units, cylinder, formula, pi (π), radius, sphere, volume
  1. from the center to the edge
  2. a rule for calculating
  3. ≈ 3.14
  4. the space inside a 3-D shape
  5. a shape with one circular base and a point
  6. the units for volume
  7. a shape with two circular bases
  8. a perfectly round ball

Part B · Show what you learned

  1. What is the volume of a cylinder with radius 3 and height 4? (π ≈ 3.14)
  2. How does a cone’s volume compare to a cylinder with the same radius and height?
  3. What measurement does a sphere’s volume depend on?
Answer key — Part A: 1) radius · 2) formula · 3) pi (π) · 4) volume · 5) cone · 6) cubic units · 7) cylinder · 8) sphere
Part B: 1) About 113.0 cubic units (3.14 × 9 × 4). 2) The cone is exactly one-third of the cylinder. 3) Only its radius.