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Volume of Cylinders, Cones, and Spheres
Students apply and compare volume formulas for solids with circular dimensions.
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Beginner
15–20 minutes
Volume & Area
Volume & Area
Page 7 of 8
Inside Cover
Volume of Cylinders, Cones, and Spheres
At a Glance
Binder SectionVolume & Area
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
How do one-third relationships connect pyramids and cones to prisms and cylinders?
Build Understanding
Cylinder: V = pi r squared h. Cone: V = one-third pi r squared h. Sphere: V = four-thirds pi r cubed.
Use the radius, not diameter, and use perpendicular height for cylinders and cones. Keep pi for exact answers or approximate only as directed.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- Cylinder V = pi r squared h.
- Cone V = 1/3 pi r squared h.
- Sphere V = 4/3 pi r cubed.
- Convert diameter to radius.
- Use cubic units.
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Interactive Vocabulary
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Worked Examples
Example 1
Cone r=4,h=9
1
V=1/3π(4²)(9)=48π cubic units.
Example 2
Sphere r=3
1
V=4/3π(27)=36π cubic units.
Ask and explain
Common Questions
Why is a cone one-third of a cylinder? They share the prism-pyramid volume relationship.
Does a sphere have a height? Use its radius in the formula.
Is pi cubed in sphere volume? No; r is cubed.
Notice and correct
Common Misconceptions
Omitting the one-third factor for cones or pyramids
Compare with a matching cylinder or prism.
Using slant height in a volume formula
Volume uses perpendicular height.
Learn Through Video
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Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
Find a pyramid’s volume when B=30 and h=12.
2
We Do
Guided Practice
Cylinder r=4,h=10: V=160 pi.
Cone r=6,h=9: V=108 pi.
Sphere r=3: V=36 pi.
Cylinder d=10,h=7: V=175 pi.
Cone with same base and height as 240-cubic-unit cylinder: V=80.
3
You Do
Independent Practice
Find a pyramid’s volume when B=30 and h=12.
Create and solve a second example with different values.
4
Stretch Your Thinking
Challenge & Real-World Practice
Compare a cone, cylinder, and sphere that share appropriate dimensions. Determine and explain their exact volume ratios.
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IXL
Volume of Cylinders, Cones, and Spheres
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