Truncated Cone Volume Calculator

Q: What is the volume of the frustum with height 5 cm and radii 1 cm and 2 cm?

36.65 cm³. To get this result you need to remember the truncated cone volume formula: V = (1/3) * π * h * (r² + r * R + R²) . Plugging in h = 5 , r = 1 , and R = 2 , we arrive at the desired result.

Creators

Anna Szczepanek, PhD

Anna Szczepanek

PhD, Jagiellonian University in Kraków, Poland

Website

Anna Szczepanek, PhD is a mathematician at the Faculty of Mathematics and Computer Science of the Jagiellonian University in Kraków, where she researches mathematical physics and applied mathematics. At Omni, Anna uses her knowledge and programming skills to create math and statistics calculators. In her free time, she enjoys hiking and reading. See full profile

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Reviewers

Davide Borchia

Physicist by education, scientist by vocation. He holds a master’s degree in complex systems physics with a specialization in quantum technologies. If he is not reading something, he is outdoors trying to enjoy every bit of nature around him. He uses his memory as an advantage, and everything you will read from him contains at least one “I read about this five years ago” moment! See full profile

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With this Omni's truncated cone volume calculator, you will never again have to wonder how to calculate the volume of a truncated cone. Here you'll find the instruction on how to apply the truncated cone volume formula as well as a step-by-step example.

Truncated cone volume formula

Recall a truncated cone (a.k.a. frustum) is a cone whose top is cut off with a plane parallel to the base. This definition gives us immediately a method of calculating the truncated cone volume: we need to subtract the volume of the smaller cone (the one we cut off) from the volume of the bigger (original) cone. What is left is the volume of the truncated cone. Easy!

Following this line of reasoning and performing some basic math operations, we arrive at the following volume formula for our truncated cone:

V = (1/3) * π * h * (r² + r * R + R²),

Where:

R is the radius of the base of the original cone (bottom surface);
r is the radius of the top surface; and
h is the height of our truncated cone.

How to use this truncated cone volume calculator?

To compute the volume of a truncated cone with our tool, you need to:

Insert the data you have. Most probably, you know the height h and the top and bottom radii: r and R, respectively.
It may happen, in more advanced problems, that you know the slant height s. Insert whatever you have!
The Omni magic happens, and the empty fields, including volume, fill in immediately.
Adjust the units if needed.

As you can see, Omni's truncated cone volume calculator is a very straightforward tool!

Similar Omni tools

Want to learn more about solids and truncated cones in particular? Make sure to check out the following Omni tools:

FAQs

What is the volume of the frustum with height 5 cm and radii 1 cm and 2 cm?

36.65 cm³. To get this result you need to remember the truncated cone volume formula: V = (1/3) * π * h * (r² + r * R + R²). Plugging in h = 5, r = 1, and R = 2, we arrive at the desired result.

How do I calculate the volume of a truncated cone?

To calculate the volume of a truncated cone, follow these steps:

Determine the top and bottom radii of your frustum: r and R, respectively.
We will also need the height h of the solid (the perpendicular distance between the two parallel surfaces).
Now, apply the formula: V = (1/3) * π * h * (r² + r * R + R²), where π ≈ 3.14.
That's it! You've just determined the volume of your frustum.