Cone Volume Calculator
Table of contents
Cone volume formulaHow to find the volume of a coneTruncated cone volume (volume of frustum)Oblique cone volumeFAQsThis cone volume calculator can help in solving your math problems or can answer your weird day-to-day questions. How much ice cream fits into my cone? How much cream can I put into the pastry bag? Or what's the volume of my conical champagne glass? If these are the questions that you would like answered, keep reading!
Cone volume formula
A cone is a solid that has a circular base and a single vertex. To calculate its volume, you need to multiply the base area (area of a circle: π × r²) by height and by 1/3:
volume = (1/3) × π × r² × h
A cone with a polygonal base is called a pyramid – see pyramid volume calculator.
How to find the volume of a cone
Let's calculate how much water fits into the conical part of the funnel.
- Determine the height of the cone (can be found using the slant height calculator). For our funnel, it's 4 in.
- Enter the base radius. It may be equal to 3 in.
- The calculator now displays the volume of the cone – in our case, it's 37.7 cu in.
Remember that you can change the units to meet your exact needs – click on the unit and select it from the list. Check out our volume converter tool if you need a simple volume unit conversion.
Truncated cone volume (volume of frustum)
A truncated cone is the cone with the top cut off, with a cut perpendicular to the height. You can calculate frustum volume by subtracting the smaller cone volume (the cut one) from the bigger cone volume (base one) or use the formula:
volume = (1/3) × π × depth × (r² + r × R + R²), whereRis the radius of the base of a cone androf the top surface radius.
An example of the volume of a truncated cone calculation can be found in our potting soil calculator, as the standard flower pot is a frustum of a cone.
Oblique cone volume
An oblique cone is a cone with an apex that is not aligned above the center of the base. It "leans" to one side, similar to the oblique cylinder. The cone volume formula of the oblique cone is the same as for the right one.
How do I calculate a cone volume by hand?
To calculate the volume of a cone, follow these instructions:
- Find the cone's base area
a. If unknown, determine the cone's base radiusr. - Find the cone's height
h. - Apply the cone volume formula:
volume = (1/3) × a × hif you know the base area, orvolume = (1/3) × π × r² × hotherwise. - Congratulations, you've successfully computed the volume of your cone!
What is the relationship between the volume of a cone and a cylinder?
If a cone and cylinder have the same height and base radius, then the volume of a cone is equal to one-third of that of the cylinder. That is, you would need the contents of three cones to fill up this cylinder. The same relationship holds for the volume of a pyramid and that of a prism (given that they have the same base area and height).
What is the volume of a typical ice cream cone?
The size of an ice cream waffle varies quite widely, yet there are a few sizes that are typical:
Radius | Height | Volume |
|---|---|---|
1 in | 6 in | 6.3 cu in |
3 cm | 11 cm | 103.7 cm³ |
2.5 cm | 11.5 cm | 75.3 cm³ |
1 7/8 in | 4 5/8 in | 17 cu in |
1 3/16 in | 6 in | 8.9 cu in |
What is the volume of cone with radius one and height three?
Recall that the cone volume formula reads:
volume = (1/3) × π × r² × h
So in our case, we have the following:
volume = (1/3) × π × 1² × 3
So the volume of our cone is exactly π! As we all know, this can be approximated as volume ≈ 3.14159.
