Welcome to our Volume of a Cylinder Calculator page.
We explain how to find the volume of a right circular cylinder and provide a quick calculator to work it out for you, step-by-step.
There are also some worked examples and some worksheets for you to practice this skill.
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This calculator finds the volume of a right circular cylinder when the radius (or diameter) and height are known.
The volume of a right circular cylinder is: \[ V = \pi r^2 h \]
where r is the radius of the circle and h is the height of the cylinder.
If you would like to see where the formula comes from, then we hope you will find the explanation below useful.
We going to look at a closed right circular cylinder and work out the volume.
The volume of a cylinder is the amount of space inside the cylinder.
To find the amount of space inside the cylinder, we need to find the area of the circular base and multiply this amount by the height.
The area of the circular base of the cylinder is: \[ A = \pi r^2 \] where A is the area and r is the radius of the circle.
The height of the cylinder is h.
This means that the volume of the cylinder is: \[ V = \pi r^2 h \]
Find the volume of the cylinder below to 1 decimal place.
The formula for the volume of a cylinder is: \[ V = \pi r^2 h \]
If we substitute the values of the radius and height into this equation, we get: \[ V = \pi \cdot 4^2 \cdot 6 = \pi \cdot 16 \cdot 6 = 96 \pi \]
This gives us a final answer of: \[ V =301.6 \;\ cm^3 \; to \; 1 \; decimal \; place \]
Find the volume of the cylinder below to 1 decimal place.
The formula for the volume of a cylinder is: \[ V = \pi r^2 h \]
As the cylinder is lying on its side, the actual 'height' of the cylinder is 6 ft and the radius is 2 ½ ft
If we substitute the values of the radius and height into this equation, we get: \[ V = \pi \cdot (2 {1 \over 2})^2 \cdot 6 = \pi \cdot {25 \over 4} \cdot 6 = {75 \over 2} \pi \]
This gives us a final answer of: \[ V = 117.8 \;\ ft^3 \; to \; 1 \; decimal \; place \]
Find the volume of the cylinder below to 2 decimal places.
We have been given the diameter instead of the radius. To find the radius, we just need to halve the diameter.
So the radius of the circular base is: \[ r = 9.4 \div 2 = 4.7 m \]
The formula for the volume of a cylinder is: \[ V = \pi r^2 h \]
If we substitute the values of the radius and height into this equation, we get: \[ V = \pi \cdot 4.7^2 \cdot 5.7 = \pi \cdot 22.09 \cdot 5.7 = 125.913 \pi \]
This gives us a final answer of: \[ V = 395.57 \;\ m^3 \; to \; 2 \; decimal \; places \]
We have created two worksheets to help you practice this skill.
The first sheet involves working out the volume of a range of cylinders where the radius is given.
The second sheet involves working out the volume of cylinders where either the radius or diameter is given.
You can check your answers to the questions on the sheets using our volume of a cylinder calculator.
Take a look at some more of our worksheets similar to these.
Here is our range of volume worksheets.
Using these sheets will help your child to:
This calculator works in the same way as the one above, but finds the volume of a pipe (which is basically an open cylinder).
The main difference is that this calculator can cope with different units of measure and you can convert the volume into liters, gallons, or fluid ounces, as well as cm3, m3, etc
This calculator works in the same way as the one above, but finds the surface area of the cylinder instead of the volume.
We have a range of area and volume calculators to help you find the area and volumes of a range of different 2d and 3d shapes.
Each calculator page comes with worked examples, formulas and practice worksheets.
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How to Print or Save these sheets
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Follow these 3 easy steps to get your worksheets printed out perfectly!
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