How to Find the Volume of a Cylinder Formula

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A cylinder is a simple geometric shape with two equally-sized and parallel circular bases. Calculating the volume of a cylinder is simple once you know the formula.^[1]

Help Finding the Volume of a Cylinder

1. 1

   Find the radius of the circular base. ^[2] 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 1 inch (2.5 cm). Write it down.

   • If you know the diameter of the circle, just divide it by 2.^[3]
   • If you know the circumference, then you can divide it by 2π to get the radius.^[4]

2. 2

   Calculate the area of the circular base. ^[5] To do this, just use the formula for finding the area of a circle, A = πr² .^[6] Just plug the radius you found into the equation. Here's how to do it:

   • A = π x 1²
   • A = π x 1
   • A = π
   • Since π is normally rounded to 3.14, you can say that the area of the circular base is 3.14 in.²

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3. 3

   Find the height of the cylinder. ^[7] 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 4 inches (10.2 cm). Write it down.

4. 4

   Multiply the area of the base by the height. ^[8] You can think of the volume of the cylinder as 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.^[9]

   • Always state your final answer in cubic units because volume is the measure of a three-dimensional space.^[10]

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Add New Question

• Question

  How do I calculate the length of the radius?

  

  The radius is half of the diameter. If you know the diameter, just divide that by two to find the radius.

• Question

  How can I find a cylinder's volume when I know height and diameter?

  

  Calculate the area of the base (which is a circle) by using the equation πr² where r is the radius of the circle. Then, multiply the area of the base by the height of the cylinder to find the volume.

• Question

  How do I calculate the volume of a water tank?

  

  Measure the tank and calculate the volume like a normal cylinder. If it's irregularly shaped, just fill it with water until it's full, and however much water you filled it is its volume.

• Question

  How can I find the height and radius of a cylinder if I only have the volume?

  

  You can't. You need at least one of either height or radius. Since the volume V of a right circular cylinder is given by V = πr²h. This leads to: h = πr²/V ; r = +√(πh/V). What the above expressions mean is that you need to know two of the variables to determine the other. Note also that if V > 0, then both r and h must also be greater than 0.

• Question

  How do I convert cubic inches to gallons?

  

  Divide by 231.

• Question

  What is the formula if only the diameter is given, but the height and volume are unknown?

  

  You can divide the diameter by 2 to get the radius, square the radius and multiply it by pi and get the area of the base, but since you don't have height or volume, you wouldn't be able to solve the equation v=bh.

• Question

  What is the volume of the cylinder if the cylinder is 1 meter full, and it's height is 20 meters, radius 1.2 meters?

  

  The volume of cylinder: r squared times pi times height= 1.2 times 1.2 times pi times 20 = 1.44 times pi times 20 which is around 90.48 meters squared. Volume of water: r squared times pi times height = 1.2 times 1.2 times pi times 1 = 1.44 times pi which is around 4.52 meters squared.

• Question

  How do I change 800 cm into meters?

  

  Divide by 100.

• Question

  Is this measured in cubic units?

  

  Yes.

• Question

  A classmate says you should use the formula (V=bh). Is this right?

  

  That's true, where "b" is the area of the circular base of the cylinder, and "h" is the cylinder's height, as explained in the final step in the above article.

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• Make sure you have accurate measurements. Double-check your work.

• The volume of a cylinder is given by the formula V = πr²h, and π is about the equivalent of 22/7 or 3.14.

• As a general rule of thumb, volume is area of the base times the height of the object. However, this will not work for shapes without equal bases, like a cone.

• Make up a few problems to practice so you know that you will get it right when you try it for real.

• This is easier with a calculator.

• 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.

• Once you've 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.

• 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. The edge of the circle should meet the zero mark in your ruler/flex tape, and the biggest measurement you obtain without losing contact with your zero mark will be the diameter.^[11]

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About This Article

Article SummaryX

1. Measure the circular base to get the diameter.
2. Divide the diameter by 2 to get the radius.
3. Calculate the area with the formula: A = πr^2, where r is the radius.
4. Measure the height of the cylinder.
5. Multiply the area by the height to get the Volume.

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How to Find the Volume of a Cylinder Formula

Source: https://www.wikihow.com/Calculate-the-Volume-of-a-Cylinder

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