Cone Calculator

Radius & Height

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Radius =

Height =

Please provide your input and click the calculate button

About the Cone Calculator

This cone calculator can calculate the volume or surface area of a cone for you. You may choose from different combinations of values to input.

Also, the calculator will tell you not just the volume/surface area, but also how to calculate it.

Usage Guide

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i. Valid Inputs

Each of the inputs provided must be a non-negative real number. In other words, the input must be 0 or greater. Here are a few examples.

Whole numbers or decimals → $\hspace{0.2em} 2 \hspace{0.2em}$ , $\hspace{0.2em} 4.25 \hspace{0.2em}$ , $\hspace{0.2em} 0 \hspace{0.2em}$ , $\hspace{0.2em} 0.33 \hspace{0.2em}$
Fractions → $\hspace{0.2em} 2/3 \hspace{0.2em}$ , $\hspace{0.2em} 1/5 \hspace{0.2em}$
Mixed numbers → $\hspace{0.2em} 5 \hspace{0.4em} 1/4 \hspace{0.2em}$

ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of what a circle is and a few different concepts related to the shape.

Cone — The Basics

A cone is a three-dimensional shape with a base (a circle in case of a circular cone) that tapers smoothly into a point at the other end (called vertex).

Surface Area and Volume of a Cone

For a cone with a radius $\hspace{0.2em} r \hspace{0.2em}$ and height $\hspace{0.2em} h \hspace{0.2em}$ , the volume is given by

V \hspace{0.25em} = \hspace{0.25em} \frac{1}{3} \pi r^2 h

And its surface area would be

S \hspace{0.25em} = \hspace{0.25em} \pi r (r + l)

Here, $\hspace{0.2em} l \hspace{0.2em}$ is the slant height of the cone. Also, the relation between $\hspace{0.2em} r \hspace{0.2em}$ , $\hspace{0.2em} h \hspace{0.2em}$ , and $\hspace{0.2em} l \hspace{0.2em}$ is

l \hspace{0.25em} = \hspace{0.25em} \sqrt{r^2 + h^2}

Examples

Example

Find the volume and surface area of an $\hspace{0.2em} 8 \text{ in} \hspace{0.2em}$ high cone with a radius of $\hspace{0.2em} 2.5 \text{ in} \hspace{0.2em}$ .

Solution

As we learned earlier, the volume of a cone is given by the formula

V \hspace{0.25em} = \hspace{0.25em} \frac{1}{3} \pi r^2 h

Substituting the values of $\hspace{0.2em} r \hspace{0.2em}$ and $\hspace{0.2em} h \hspace{0.2em}$ , we get

\begin{align*} V \hspace{0.25em} &= \hspace{0.25em} \frac{1}{3} \pi \cdot 2.5^2 \cdot 8 \\[1.5em] &= \hspace{0.25em} 52.36 \end{align*}

So the volume of the cone is $\hspace{0.2em} 52.36 \text{ in}^3 \hspace{0.2em}$ .

Now for the cone's surface area, the formula is

S \hspace{0.25em} = \hspace{0.25em} \pi r (r + l)

But the question doesn't provide us the value of the slant height $\hspace{0.2em} l \hspace{0.2em}$ . So, we'll need to calculate it using the cone's radius and height.

\begin{align*} l \hspace{0.25em} &= \hspace{0.25em} \sqrt{r^2 + h^2} \\[1em] &= \hspace{0.25em} \sqrt{2.5^2 + 8^2} \\[1em] &= \hspace{0.25em} 8.38 \end{align*}

Plugging the values of $\hspace{0.2em} r \hspace{0.2em}$ and $\hspace{0.2em} r \hspace{0.2em}$ into the formula for surface area, we have

\begin{align*} S \hspace{0.25em} &= \hspace{0.25em} \pi r (r + l) \\[1em] &= \hspace{0.25em} \pi \cdot 2.5 \cdot (2.5 + 8.38) \\[1em] &= \hspace{0.25em} 85.45 \end{align*}

The surface area of the cone is $\hspace{0.2em} 85.45 \text{ in}^2 \hspace{0.2em}$ .