Welcome to our Volume of a Cone Calculator page.
We explain how to find the volume of a right cone and provide a quick calculator to work it out for you, step-by-step.
There are also some worked examples and practice worksheets on this page to help you master this skill.
Quicklinks to ...
Our calculator finds the volume of a right circular cone when the radius (or diameter) and height are known.
There are many different types of cones, including right cones, oblique cones and elliptic cones.
The cones that are most common, and that we use for our volume of a cone calculator, are right circular cones, which is a cone with a circular base whose apex (highest point) is directly above the center of the base.
The volume of a cone is: \[ V = {1 \over 3} \pi r^2 h \]
where r is the radius of the circle and h is the perpendicular height of the cone.
Find the volume of the cone below. Give your answer to 1 decimal place.
The height of the cone is 12 cm. The radius is 4 cm.
The formula for the volume of a closed cone is: \[ V = {1 \over 3} \pi r^2 h \]
If we substitute the values of the radius and height into the formala, we get: \[ V = {1 \over 3} \pi \cdot 4^2 \cdot 12 \]
If we simplify this, we get: \[ V = {1 \over 3} \pi \cdot 16 \cdot 12 = {1 \over 3} \pi \cdot 192 = 64 \pi\]
This gives us a final answer of: \[ V = 201.1 \;\ cm^3 \;\ to \;\ 1 \;\ decimal \;\ place \]
Find the volume of the cone below to 1 decimal place.
The cone is lying on its side. The actual height of the cone is 10 inches. The radius is 4 ½ inches.
The formula for the volume of a closed cone is: \[ V = {1 \over 3} \pi r^2 h \]
If we substitute the values of the radius and height into the formala, we get: \[ V = {1 \over 3} \pi \cdot (4{ 1 \over 2})^2 \cdot 10 \]
If we simplify this, we get: \[ V = {1 \over 3} \pi \cdot {81 \over 4} \cdot 10 = {1 \over 3} \pi \cdot {405 \over 2} = {135 \over 2} \pi \]
This gives us a final answer of: \[ V = 212.1 \;\ in^3 \;\ to \;\ 1 \;\ decimal \;\ place \]
Find the volume of the cone below to 2 decimal places.
The height of the cone is 4.8 meters. The diameter of the cone is 4.6 meters.
To find the radius, we divide the diameter by 2. So the radius = 4.8 ÷ 2 = 2.4 meters.
The formula for the volume of a closed cone is: \[ V = {1 \over 3} \pi r^2 h \]
If we substitute the values of the radius and height into the formala, we get: \[ V = {1 \over 3} \pi \cdot (2.3)^2 \cdot 4.8 \]
If we simplify this, we get: \[ V = {1 \over 3} \pi \cdot 5.29 \cdot 4.8 = {1 \over 3} \pi \cdot 25.392 = 8.464 \pi \]
This gives us a final answer of: \[ V = 26.59 \;\ m^3 \;\ to \;\ 2 \;\ decimal \;\ places \]
Find the volume of the witch's black hat shown below. Give your answer to the nearest cm3.
The height of the cone is 62 cm. The diameter of the cone is 18 cm.
To find the radius, we divide the diameter by 2. So the radius = 18 ÷ 2 = 9 cm.
The formula for the volume of a closed cone is: \[ V = {1 \over 3} \pi r^2 h \]
If we substitute the values of the radius and height into the formala, we get: \[ V = {1 \over 3} \pi \cdot 9^2 \cdot 62 \]
If we simplify this, we get: \[ V = {1 \over 3} \pi \cdot 81 \cdot 62 = {1 \over 3} \pi \cdot 5022 = 1674 \pi \]
This gives us a final answer of: \[ V = 5259 \;\ cm^3 \;\ to \;\ the \;\ nearest \;\ cm^3 \]
We have created two worksheets for you to practice the skill of finding the volume of a range of different right circular cones.
Sheet 1: you have to find the volume of different cones using the height and radius measurements.
Sheet 2: you have to find the volume of different cones using the height and radius or diameter measurements.
You can use our volume of a cone calculator to check you working out if you get stuck!
Take a look at some more of our worksheets similar to these.
We also have a surface area of a cone calculator which works in a similar way to the calculator on this page.
Here is our range of volume worksheets.
Using these sheets will help your child to:
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.
We have a range of other area worksheets and support pages for a range of different 2d shapes.
How to Print or Save these sheets
Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!
How to Print or Save these sheets
Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!
The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.
We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.
Looking for some fun printable math games?
We have some great games for you to play in our Math Games e-books!
Do you know how old you are...in weeks? days? hours?
Are you more than a million minutes old?
Find out how old you are to the nearest second!
We have updated and improved our fraction calculators to show you how to solve your fraction problems step-by-step!
Take a look and try them out!
Have a look at some of our most popular pages to see different Math activities and ideas you could use with your child
If you are a regular user of our site and appreciate what we do, please consider making a small donation to help us with our costs.
Get a free sample copy of our Math Salamanders Dice Games book with each donation!
Looking for a fun and motivating way to learn and practice math skills?
Why not try one of our free printable math games with your students!
New! Comments
Have your say about the Math resources on this page! Leave me a comment in the box below.