Resources/Volume formulas for cones, cylinders, and spheres
Grade 8•Printable worksheet + answer key•CC0 license

Volume formulas for cones, cylinders, and spheres

Practice volume formulas using radius and height.

Students apply volume formulas for curved 3D shapes using pi approximations.

Print-ready worksheet with answer key and quick teaching tips.

Grade 80 problems10 minAnswer key included
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Ready-to-teach

Clear steps, examples, and practice in one printable page.

Misconception-proof

Highlights common mistakes and how to fix them quickly.

Open license

CC0: free to copy, adapt, and share without attribution.

Quick overview

This free volume formulas worksheet for grade 8 covers cylinders, cones, and spheres with step-by-step practice.

Lesson plan snapshot

15-20 min
  • Warm-up (3 min): review circle area and radius vs diameter.
  • Model (5 min): solve the worked example together.
  • Guided practice (5 min): complete problems 1-3 as a group.
  • Independent practice (7 min): finish the remaining problems.

Materials: calculator, pencil

Learning targets

  • Use V = pi r^2 h for cylinders.
  • Use V = (1/3) pi r^2 h for cones.
  • Use V = (4/3) pi r^3 for spheres.
  • Label volume in cubic units and compare results.

Step-by-step approach

  1. 1Identify the shape and write the correct volume formula.
  2. 2Check whether the radius or diameter is given.
  3. 3Substitute values and use pi approx 3.14.
  4. 4Compute and label the answer in cubic units.

Common mistakes

Mistake

Using diameter instead of radius.

Try instead

Radius is half the diameter; use r in every formula.

Mistake

Forgetting the one-third in the cone formula.

Try instead

A cone is one-third of a cylinder with the same base and height.

Mistake

Mixing surface area and volume formulas.

Try instead

Volume uses r^2 or r^3 and has cubic units.

Worked example

Guided
Find the volume of a cylinder with radius 3 and height 8. Use pi approx 3.14.
  1. Write the formula: V = pi r^2 h.
  2. Substitute: V = 3.14 × 3^2 × 8 = 3.14 × 9 × 8.
  3. Compute: 3.14 × 72 = 226.08.
Answer: 226.08 cubic units

Related resources

Geometry

Shape properties and geometry foundations.

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Area & perimeter

Build confidence with area formulas and units.

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Word problems

Apply formulas in context-rich scenarios.

View resource

Practice problems

10 problems • 15 min

Printable worksheet
  1. 1
    Find the volume of a cone with radius 8 and height 8. Use pi approx 3.14.
  2. 2
    Sphere A has radius 6. Sphere B has radius 4. Which has the greater volume?
  3. 3
    A cone and a cylinder have the same radius 3 and height 4. How many times larger is the cylinder's volume?
  4. 4
    A sphere has diameter 10. Find the volume. Use pi approx 3.14.
  5. 5
    A cylinder has diameter 10 and height 10. Find the volume. Use pi approx 3.14.
  6. 6
    Find the volume of a cylinder with radius 4 and height 11. Use pi approx 3.14.
  7. 7
    A cylinder has diameter 12 and height 10. Find the volume. Use pi approx 3.14.
  8. 8
    Sphere A has radius 3. Sphere B has radius 4. Which has the greater volume?
  9. 9
    Find the volume of a cylinder with radius 8 and height 11. Use pi approx 3.14.
  10. 10
    A cone and a cylinder have the same radius 2 and height 10. How many times larger is the cylinder's volume?

Answer key

10 answers
  1. 11) 535.89
  2. 22) Sphere A
  3. 33) 3
  4. 44) 523.33
  5. 55) 785
  6. 66) 552.64
  7. 77) 1130.4
  8. 88) Sphere B
  9. 99) 2210.56
  10. 1010) 3

Teacher tips

  • THave students write the formula before substituting values.
  • TUnderline the radius in each problem to avoid diameter mistakes.
  • TDiscuss why cone volume is one-third of a cylinder.

Parent tips

  • PAsk your child to explain which formula they chose and why.
  • PPractice halving the diameter to find the radius.
  • PUse real objects like cans and balls to talk about volume.

Open license

You are free to copy, adapt, and share these materials. No attribution required. Released under Creative Commons CC0 1.0 (public domain).