The volume of a cylinder measures the total space inside it. You calculate it with the formula V = π × r² × h, where r is the base radius and h is the height. The result is always in cubic units (cm³, m³, in³, ft³). This worksheet gives you a full lesson, three worked examples, and 10 graded practice problems with a downloadable PDF and answer key.

• Understand why the cylinder volume formula works.
• Follow a 4-step method that works for every problem.
• Avoid the three most common errors students make.
• Practice with 10 graded problems and check your answers instantly.

Where This Formula Comes From

This idea goes back to Archimedes of Syracuse (c. 287-212 BCE), who proved that the volume of a cylinder equals the area of its circular base multiplied by its height. He derived this by imagining the cylinder as an infinite stack of infinitely thin circular discs — a concept that foreshadowed integral calculus by nearly two thousand years.

The base of a cylinder is a circle, so its area is πr². Stack that circle to a height of h, and you get V = πr² × h. Archimedes was so proud of this result that he reportedly asked for a cylinder circumscribing a sphere to be engraved on his tomb.

Today the same formula appears in engineering (pipe capacity, tank design), medicine (lung volume estimation), and everyday life (how much a can of soup holds). That is why it earns a dedicated place in every middle school geometry curriculum worldwide.

        ___________
       /           \
      /      r      \      <-- circular base, area = pi * r^2
     |       +-------|
     |       |       |
     |       | h     |      <-- height
     |       |       |
      \      |      /
       \_____|_____/

  V = pi * r^2 * h
    = (area of base) * height
    

What Is the Volume of a Cylinder?

The volume of a cylinder is the total amount of three-dimensional space enclosed inside it, measured in cubic units. A cylinder has two congruent circular bases connected by a curved lateral surface; its volume depends only on the radius of those bases and the perpendicular distance between them (the height).

Think of a cylinder as a circular prism. Just as the volume of any prism equals (base area) × height, the cylinder’s volume equals (πr²) × h. This connection makes the formula easy to remember and easy to extend to other 3-D shapes.

How Do You Calculate the Volume of a Cylinder? (Step-by-Step)

Follow these four steps for every cylinder volume problem, and you will not make errors.

1. Identify r and h. Read the problem carefully. Write down the radius r and the height h. If the problem gives you the diameter, divide it by 2 to get r before doing anything else.
2. Square the radius. Calculate r² = r × r. Do this step separately to avoid arithmetic errors.
3. Multiply by π. Multiply r² by π (use 3.14159 or the π key on your calculator). This gives you the area of the circular base.
4. Multiply by height. Multiply the base area by h. Write the answer with the correct cubic unit.

3 Fully Worked Examples

What Are the Most Common Mistakes in Cylinder Volume Problems?

Three errors account for the vast majority of lost marks on cylinder volume questions. Recognising them before you sit a test is the fastest way to protect your score.

On-Page Practice Worksheet: 10 Cylinder Volume Problems

Work through the problems below in order. Show each step. Use π = 3.14159 and round to two decimal places unless the problem states otherwise. When you are done, expand the Answer Key to check your work.

How to use this worksheet: Print the PDF (button below) or work directly on screen. Attempt every problem before checking the answer key. If you get a problem wrong, go back to the worked examples and identify which step you missed.

1. A cylinder has radius r = 3 cm and height h = 5 cm. Find its volume.
2. A cylinder has radius r = 4 cm and height h = 10 cm. Find its volume.
3. A cylinder has diameter d = 6 m and height h = 8 m. Find its volume.
4. A cylinder has radius r = 7 in and height h = 3 in. Find its volume.
5. A cylindrical water tank has diameter d = 10 ft and height h = 6 ft. Find its volume.
6. A cylinder has radius r = 2.5 cm and height h = 12 cm. Find its volume.
7. A cylinder has radius r = 5 m and height h = 5 m. Find its volume.
8. A cylinder has volume V = 628.32 cm³ and radius r = 5 cm. Find its height.
9. A cylinder has volume V = 1,570.80 in³ and height h = 20 in. Find its radius.
10. A solid metal cylinder has radius r = 6 cm and height h = 14 cm. A cylindrical hole of radius r = 2 cm and the same height is drilled through its centre. Find the volume of the remaining solid.