Please provide your input and click the calculate button

Show SolutionHide Solution

About the Volume Calculator

This volume calculator lets you calculate the volume for several different solid shapes. The shapes currently supported are cones, cubes, cuboids (rectangular prisms), cylinders, and spheres.

For most shapes, you have the option to choose what combination of inputs you want to provide. And to top it all, the calculator will give you not just the answer, but also the step by step solution.

Usage Guide

ShowHide

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.

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 the concept of volume and its formula for a few important shapes.

Volume — Concept and Formulas

The volume of any three-dimensional or solid figure is a the amount of space it occupies.

Let's look at the formulas for the volumes of the some of the most common solid shapes.

Volume of a Cone

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

For a cube with an edge-length of $\hspace{0.2em} a \hspace{0.2em}$, the volume would be,

$V \hspace{0.25em} = \hspace{0.25em} a^3$

Volume of a Cuboid (Rectangular Prism)

The formula for the volume of a cuboid (or rectangular prism) with a length $\hspace{0.2em} l \hspace{0.2em}$, width $\hspace{0.2em} w \hspace{0.2em}$, height $\hspace{0.2em} h \hspace{0.2em}$ is

$V \hspace{0.25em} = \hspace{0.25em} l \cdot w \cdot h$

Volume of a Cylinder

The volume of a cylinder with a radius $\hspace{0.2em} r \hspace{0.2em}$ and height $\hspace{0.2em} h \hspace{0.2em}$ is

$V \hspace{0.25em} = \hspace{0.25em} \pi r^2 h$

Volume of a Sphere

The sphere of radius $\hspace{0.2em} r \hspace{0.2em}$ has a volume equal to

A rectangular prism has dimensions of length $\hspace{0.2em} 10 \hspace{0.2em}$ meters, width $\hspace{0.2em} 4 \hspace{0.2em}$ meters, and height $\hspace{0.2em} 6 \hspace{0.2em}$ meters. Calculate its volume.

Solution

The formula for the volume of a rectangular prism is

$V \hspace{0.25em} = \hspace{0.25em} l \cdot w \cdot h$

So, the volume of the rectangular prism is $\hspace{0.2em} 240 \text{ m}^3 \hspace{0.2em}$.

Example

Calculate the volume of a cone with a radius of $\hspace{0.2em} 5 \text{ in} \hspace{0.2em}$ and a height of $\hspace{0.2em} 8 \text{ in} \hspace{0.2em}$.

So, the volume of the sphere is $\hspace{0.2em} 143.79 \text{ cm}^3 \hspace{0.2em}$.

Example

A $\hspace{0.2em} 10 \hspace{0.2em}$ centimetres high cylindrical tank has a volume of $\hspace{0.2em} 40 \pi \text{ cm}^3 \hspace{0.2em}$. Calculate the volume of the tank.

Solution

The formula for a cylinder's volume is

$V \hspace{0.25em} = \hspace{0.25em} \pi r^2 h$

Rarranging the formula to make $\hspace{0.2em} r \hspace{0.2em}$ its subject, we have