Calculate the Volume of a Cylinder

A cylinder is a simple geometric shape with two equally-sized and parallel circular bases. This article will teach you how to calculate the volume of a cylinder.

10 Second Summary

1. Find the radius of the circular base. More ↓
2. Calculate the area of the circular base. ↓
3. Find the height of the cylinder. ↓
4. Multiply the area of the base by the height. ↓
5. State your final answer in cubic units.

Steps

Help Finding the Volume of a Cylinder

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Calculating the Volume of a Cylinder

  1. Find the radius of the circular base. Either circle will do since they are the same size. If you already know the radius, you can move on. If you don't know the radius, then you can use a ruler to measure the widest part of the circle and then divide it by 2. This will be more accurate than trying to measure half of the diameter. Let's say that the radius of this cylinder is {{safesubst:#invoke:convert|convert}}. Write it down.
    • If you know the diameter of the circle, just divide it by 2.
    • If you know the circumference, then you can divide it by 2π to get the radius.
  2. Calculate the area of the circular base. To do this, just use the formula for finding the area of a circle, A = πr2. Just plug the radius you found into the equation. Here's how to do it:
    • A = π x 12 =
    • A = π x 1.
    • Since π is approximately 3.14 to three digits, you can say that the area of the circular base is 3.14 in.2
  3. Find the height of the cylinder. If you know the height already, move on. If not, use a ruler to measure it. The height is the distance between the edges of the two bases. Let's say the height of the cylinder is {{safesubst:#invoke:convert|convert}}. Write it down.
  4. Multiply the area of the base by the height. You can think of the volume of the cylinder as the volume of the area of the base being extended throughout the height of the cylinder. Since you know that the area of the base is 3.14 in.2 and that the height is 4 in., you can just multiply the two together to get the volume of the cylinder. 3.14 in.2 x 4 in. = 12.56 in.3 This is your final answer.
    • Always state your final answer in cubic units because volume is the measure of a three-dimensional space.



Tips

  • As a general rule of thumb, volume is area of the base times the height of the object. (this may not work in every case, such as a cone.)
  • Make up a few problems to practice so you know that you will get it right when you try it for real.
  • It may be easier to measure the diameter and divide by 2 in order to get an accurate radius without needing to find the exact center.
  • Remember the diameter is the biggest chord in a circle or in a circumference, i.e. the biggest measurement you can get between two points in a circumference or in the circle within. So make the edge of the circle meet the zero mark in your ruler/flex tape and the biggest measurement you obtain without losing contact with your zero mark, that's the diameter.
  • This is easier with a calculator.
  • Once you calculated the area of the circle, consider the multiplication by the height as height stacking. In other words, you're basically stacking the base circle up until it reaches the height of the cylinder, and because you've calculated the area, this equals the volume.
  • The volume of a cylinder is given by the formula V = πr2h, and π is about the equivalent of 22/7.
  • Make sure you have accurate measurements.

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