How much water fits in a soup can, a paper funnel, or a rubber ball? Each shape holds a different amount of space, and volume is the number that measures it. The good news is that the volume of a cylinder, cone, and sphere all come from the same building block: the radius of a circle. Once you know three short formulas, you can find how much any of these round solids holds.
Cylinder: V = pi x r^2 x h. Cone: V = (1/3) x pi x r^2 x h. Sphere: V = (4/3) x pi x r^3. Here r is the radius and h is the height, pi is about 3.14159, and volume comes out in cubic units. A cone is exactly one third of the cylinder that shares its radius and height.
Volume Basics: What Cubic Units Mean
Volume is the amount of space inside a solid shape. It answers the question of how much a shape can hold, like water in a bottle or air in a ball.
Volume is always measured in cubic units. If your lengths are in centimeters, the volume is in cubic centimeters, written as cm^3. If your lengths are in inches, the volume is in cubic inches, or in^3. The small 3 means three directions of space: length, width, and height.
Two facts make the three shapes on this page a family. Each one is round, so each uses pi, the number about 3.14159 that links a circle to its size. And each one starts from the radius r, the distance from the center of a circle to its edge. Keep every measurement in the same unit before you start, and your answer will land in the matching cubic unit.
Volume of a Cylinder
A cylinder is a shape with two flat circular ends and straight sides, like a can or a pipe. Its volume is the area of the circular base times the height.
The area of a circle is pi x r^2, so the volume formula is:
V = pi x r^2 x h
Here r is the radius of the circle and h is the height of the cylinder. Follow these steps to use it.
- Square the radius: multiply r by itself.
- Multiply that by pi (about 3.14159).
- Multiply the result by the height h.
Worked example. A can has a radius of 3 cm and a height of 10 cm.
- r^2 = 3 x 3 = 9
- pi x 9 = 3.14159 x 9 = 28.2743
- 28.2743 x 10 = 282.74
The cylinder holds about 282.74 cm^3, rounded to two decimal places.
Volume of a Cone
A cone has one circular base that narrows to a single point, like an ice cream cone or a funnel. It fills less space than a cylinder of the same size.
In fact, a cone holds exactly one third of the matching cylinder. So the formula is the cylinder formula with a one third in front:
V = (1/3) x pi x r^2 x h
Here r is the radius of the base and h is the straight height from the base to the tip. The steps are the same as the cylinder, plus one more.
- Square the radius: r x r.
- Multiply by pi, then by the height h.
- Divide that result by 3, or multiply by one third.
Worked example. A funnel has a radius of 3 cm and a height of 10 cm, the same as the can above.
- pi x r^2 x h = 3.14159 x 9 x 10 = 282.74
- 282.74 / 3 = 94.25
The cone holds about 94.25 cm^3. Notice that this is exactly one third of the cylinder’s 282.74 cm^3.
Volume of a Sphere
A sphere is a perfectly round ball, like a marble or a globe. Every point on its surface sits the same distance r from the center, so its volume depends only on the radius.
The formula uses r cubed, which means the radius multiplied by itself three times:
V = (4/3) x pi x r^3
A sphere has no separate height to measure, which makes it the simplest of the three. Here is how to work it out.
- Cube the radius: r x r x r.
- Multiply by pi (about 3.14159).
- Multiply by 4, then divide by 3.
Worked example. A ball has a radius of 3 cm.
- r^3 = 3 x 3 x 3 = 27
- pi x 27 = 3.14159 x 27 = 84.823
- 84.823 x 4 / 3 = 339.29 / 3 = 113.10
The sphere holds about 113.10 cm^3, rounded to two decimal places.
Quick Comparison: Cylinder vs Cone
The cone and cylinder are close relatives. With the same radius and height, the cone is always one third of the cylinder. That single fact ties two of the three formulas together.
The table below uses our worked numbers, with r = 3 and h = 10.
| Shape | Formula | Volume (r = 3, h = 10) |
|---|---|---|
| Cylinder | V = pi x r^2 x h | 282.74 cm^3 |
| Cone | V = (1/3) x pi x r^2 x h | 94.25 cm^3 (one third) |
So once you have a cylinder’s volume, divide by 3 to get the matching cone. To reverse it, multiply the cone by 3.
How Volume Differs From Area and Circumference
Volume is a 3D idea, so it differs from the flat measures of a shape. Area covers a flat region in square units. Circumference is the distance around a circle, measured in plain length units. Volume fills a solid in cubic units, so all three answer different questions.
For the space on a surface, see our guide on how to find the area of any shape. For the distance around a circle, visit how to find the circumference of a circle.
Want the answer without the arithmetic? Enter your radius and height into our Volume Calculator and it returns the volume of a cylinder, cone, or sphere in one click, with the units handled for you.
Frequently Asked Questions About Volume
What Is the Formula for the Volume of a Cylinder?
The volume of a cylinder is V = pi x r^2 x h, where r is the radius of the circular base and h is the height. You find the area of the base circle with pi x r^2, then multiply by the height. The answer comes out in cubic units, such as cm^3.
How Do You Find the Volume of a Cone?
Use V = (1/3) x pi x r^2 x h. First find pi x r^2 x h, just like a cylinder, then divide the result by 3. For example, a cone with r = 3 and h = 10 gives 282.74 divided by 3, which is about 94.25 cubic units.
What Is the Formula for the Volume of a Sphere?
The volume of a sphere is V = (4/3) x pi x r^3, where r is the radius. Cube the radius, multiply by pi, then multiply by 4 and divide by 3. A sphere needs only the radius, since it has no separate height to measure.
Why Is a Cone One Third of a Cylinder?
When a cone and a cylinder share the same radius and the same height, three of those cones fill the cylinder exactly. That is why the cone formula is the cylinder formula times one third. It is a fixed geometric fact that holds for any matching pair.
What Value of Pi Should I Use?
For most work, pi is about 3.14159, and rounding to a few decimals is fine. Using more digits makes little difference for everyday problems. Because pi never ends, any volume with a circle in it is an approximation, so round your final answer sensibly and note that you did.
What Units Does Volume Use?
Volume is always in cubic units, written with a small 3, such as cm^3 or in^3. Keep every length in the same unit before you calculate. If your radius and height are in centimeters, the volume will be in cubic centimeters automatically.
Do I Use Radius or Diameter in These Formulas?
Always use the radius, which is half of the diameter. If a problem gives you the diameter, divide it by 2 first. For example, a ball 6 cm across has a radius of 3 cm, and you use 3 in the sphere formula, not 6.
Sources
Authoritative Sources Used in This Article
This article is for general education only. Always double-check the formulas and math for your own problem before you rely on the result. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 11, 2026.
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Shakeel Muzaffar is the Founder and Editor-in-Chief of MultiCalculators.com, bringing over 15 years of experience in digital publishing, product strategy, and online tool development. He leads the platform's editorial vision, ensuring every calculator meets strict standards for accuracy, usability, and real-world value. Shakeel personally oversees content quality, formula verification workflows, and the platform's commitment to publishing tools that are genuinely useful for students, professionals, and everyday users worldwide.
