Volume of a Cylinder

In this tutorial, we will learn how to find the volume of a cylinder. So let's start with what a cylinder typically looks like.

A cylinder

So you have two circular and parallel surfaces (bases) joined by a uniform circular cross-section - all of the same radius.

Now a cylinder whose axis - the line joining the centers of the bases - is perpendicular to the bases, is known as a right cylinder or a right circular cylinder.

Right and Oblique Cylinders

As is generally the case, for the rest of the tutorial, we'll use the word cylinder to refer to a right circular cylinder.

Volume of a Cylinder

As with any three-dimensional solid, the volume of a cylinder is the total amount of space the cylinder occupies.

Formula for Volume of a Cylinder

Cylinder - Dimensions

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

V=43πr3V = \frac{4}{3} \pi r^3
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For any solid with a uniform cross-section, the volume is given by -

V=Abh(1)V = A_b \cdot h \hspace{0.25cm} \rule[0.1cm]{1cm}{0.1em} \hspace{0.15cm} (1)

where Ab\hspace{0.2em} A_b \hspace{0.2em} is the area of cross-section and h\hspace{0.2em} h \hspace{0.2em} is the length of the solid perpendicular to the cross-section.

For the cylinder with a radius r\hspace{0.2em} r \hspace{0.2em}, the area of cross-section would be,

Ab=πr2(2)A_b = \pi r^2 \hspace{0.25cm} \rule[0.1cm]{1cm}{0.1em} \hspace{0.15cm} (2)

Combining (1)\hspace{0.2em} (1) \hspace{0.2em} and (2)\hspace{0.2em} (2) \hspace{0.2em}, we get the volume

V=πr2hV = \pi r^2 h

How to Find the Volume of a Cylinder | Examples

Now, let's use what we've learned so far to solve a couple of examples.


A cylinder has a radius of 3\hspace{0.2em} 3 inches and a height of 10\hspace{0.2em} 10 inches. Find its volume.


We need to find the volume here, so we start with the formula.

V=πr2hV = \pi r^2 h

And plugging in the values for r\hspace{0.2em} r \hspace{0.2em} and h\hspace{0.2em} h \hspace{0.2em}, we get -

V=π3210=282.74\begin{align*} V &= \pi \cdot 3^2 \cdot 10 \\[1em] &= 282.74 \end{align*}

So the volume of the cylinder is 282.74 in2\hspace{0.2em} 282.74 \text{ in}^2.


28π\hspace{0.2em} 28 \pi \hspace{0.2em}cubic centimeters of metal was melted and cast into an 8\hspace{0.2em} 8 cm high cylinder. Calculate the radius of the cylinder.


Here's the key to solving this question.

When we melt some metal and cast it into a cylinder (or any other shape), the volume of the cylinder would be the same as the volume of the metal we started with. Assuming there are no losses in the process.

So indirectly, the question tells us the volume (V)\hspace{0.2em} (V) \hspace{0.2em} of the cylinder is 28π cm3\hspace{0.2em} 28 \pi \text{ cm}^3 \hspace{0.2em}.

It also tells us the height (h)\hspace{0.2em} (h) \hspace{0.2em} of the cylinder formed – 88 cm.

So let's substitute the values of V\hspace{0.2em} V \hspace{0.2em} and h\hspace{0.2em} h \hspace{0.2em} into our formula for volume.

V=πr2h28π=πr27r2=4\begin{align*} {\color{Red} V} &= \pi \cdot r^2 \cdot {\color{Teal} h} \\[1em] {\color{Red} 28 \pi} &= \pi \cdot r^2 \cdot {\color{Teal} 7} \\[1em] r^2 &= 4 \end{align*}

Taking the square root on both sides –

r=2r = 2

Note – We don't need to worry about the negative square root since the radius cannot be negative.

And with that, we come to the end of this tutorial on the volume of a cylinder. Until next time.