Volume of a Cone Calculator
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.
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Volume of a Cone Calculator
Our calculator finds the volume of a right circular cone when the radius (or diameter) and height are known.
How the Volume of a Cone Calculator Works
- Select if you want to use the radius or diameter (default is radius).
- For the value, you can choose a whole number, decimal or fraction.
- You can type a fraction by typing the numerator then '/' then the denominator.
- You can type a mixed number by typing the whole-number part, then a space then the fraction part.
- Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).
- Choose your units of measurement (default is none)
- Choose your desired accuracy (default is 2 decimal places)
- Click the Find Volume button
- You will be given two answers for the area, one in terms of Pi (π) and the other answer as a decimal value.
Types of Cones
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.
Volume of a Cone Formula
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.
Volume of a Cone Examples
Volume of a Cone Example 1
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: \[ V = 201.1 \;\ cm^3 \;\ to \;\ 1 \;\ decimal \;\ place \]
Volume of a Cone Example 2
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: \[ V = 212.1 \;\ in^3 \;\ to \;\ 1 \;\ decimal \;\ place \]
Volume of a Cone Example 3
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: \[ V = 26.59 \;\ m^3 \;\ to \;\ 2 \;\ decimal \;\ places \]
Volume of a Cone Example 4
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: \[ V = 5259 \;\ cm^3 \;\ to \;\ the \;\ nearest \;\ cm^3 \]
Volume of a Cone Worksheets
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!
More Recommended Math Worksheets
Take a look at some more of our worksheets similar to these.
Surface Area of a Cone Calculator
We also have a surface area of a cone calculator which works in a similar way to the calculator on this page.
More Volume Worksheets
Here is our range of volume worksheets.
Using these sheets will help your child to:
- know what volume is and how to find it;
- find the volume of simple shapes by counting cubes;
- find the volume of rectangular prisms;
- solving basic problems involving volume
More Area & Volume Calculators
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.
More Area Support and Resources
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
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How to Print or Save these sheets
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Follow these 3 steps to get your worksheets printed perfectly!
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