Cylinder volume calculator

What is cylinder volume?

The volume of a cylinder refers to the amount of space enclosed within its boundaries. In geometry, a cylinder is one of the most straightforward 3D shapes obtained by extending a circle along a third dimension, called the height. There are different types of cylinders, such as right cylinders, where the sides are perpendicular to the base, and oblique cylinders, where the sides lean over. Hollow cylinders also exist, characterized by a cylindrical shell enclosing an empty space, with both external and internal radii.

Calculating the volume of a cylinder is a common task in both academic settings and various industries. Whether you’re dealing with the volume of a storage tank or computing the space in a cylindrical packaging, understanding how to calculate cylinder volume is essential.

Types of cylinders

Right circular cylinder is defined by having circular bases aligned directly above one another, and the sides are perpendicular to the base. It is the most common type of cylindrical object.

Oblique cylinder differs from a right cylinder in that its sides are not perpendicular to the bases. Instead, they lean over, resembling a slanted appearance.

Hollow cylinder has two concentric circles forming its cross-section, leading to both an external and internal diameter.

Formulas

The formula for calculating the cylinder’s volume varies depending on the type of cylinder:

Right and oblique cylinder

To find the volume of a right or oblique cylinder, use the formula:

$V = \pi r^2 h$

Where:

• $V$ is the volume.
• $r$ is the radius of the base.
• $h$ is the height of the cylinder.

Alternatively, if the diameter ($d$) is known, the formula is:

$V = \pi \left(\frac{d}{2}\right)^2 h$

Hollow cylinder

For a hollow cylinder, the volume is obtained by subtracting the volume of the inner empty cylinder from the volume of the outer cylinder:

$V = \pi h (r_1^2 - r_2^2)$

Where:

• $r_1$ is the external radius.
• $r_2$ is the internal radius.

Examples

Example 1: Right circular cylinder

Calculate the volume of a right circular cylinder with a radius of 4 meters and a height of 10 meters.

$V = \pi (4^2) \cdot 10 = \pi \cdot 16 \cdot 10 = 160\pi$

Considering $\pi \approx 3.14159$:

$V \approx 502.65 \text{ cubic meters}$

Example 2: Hollow cylinder

Calculate the volume of a hollow cylinder with an external diameter of 8 cm, an internal diameter of 4 cm, and a height of 15 cm.

First, convert diameters to radii:

• External radius $r_1 = \frac{8}{2} = 4$ cm
• Internal radius $r_2 = \frac{4}{2} = 2$ cm

Now, calculate the volume:

$V = \pi \cdot 15 \cdot (4^2 - 2^2) = \pi \cdot 15 \cdot (16 - 4) = \pi \cdot 15 \cdot 12 = 180\pi$

Considering $\pi \approx 3.14159$:

$V \approx 565.49 \text{ cubic centimeters}$

Example 3: Calculate the volume of a wine barrel

Imagine a large wine barrel shaped like a cylinder used by a winery to hold vintage wine. The barrel has a diameter of 2 meters and a height of 3 meters. To find out how much wine it can hold, you need to calculate its volume.

Using the formula for a cylinder’s volume:

$V = \pi \left(\frac{2}{2}\right)^2 \cdot 3 = \pi \cdot 1^2 \cdot 3 = 3\pi$

Considering $\pi \approx 3.14159$:

$V \approx 9.42 \text{ cubic meters}$

This means the wine barrel can hold approximately 9.42 cubic meters of wine, which is equivalent to over 9,000 liters!

Volume units

Cylinder volume can be expressed in various units of measure, such as cubic meters, cubic centimeters, liters, or gallons, depending on the context or industry. The choice of units often depends on the size of the cylinder and the precision required. For easy conversion between different volume units, you can utilize a volume unit converter.

Notes

• Ensure units are consistent when calculating volume. If using mixed units (e.g., centimeters and meters), convert them into one unit system before performing calculations or use our automatic unit conversions.
• Remember that cylinder volume calculation is directly proportional to the height and the square of the radius for right cylinders.
• The precision of the outcome can be influenced by the value used for $\pi$. For many practical purposes, using $\pi \approx 3.14159$ is sufficient.

Frequently asked questions

How do you find the volume of an oval cylinder?

An oval cylinder, also known as an elliptical cylinder, has an elliptical base. To find its volume, use the formula:

$V = \pi a b h$

Where:

• $a$ is the semi-major axis of the ellipse.
• $b$ is the semi-minor axis of the ellipse.
• $h$ is the height of the cylinder.

Note that an elliptical cylinder is not a circular cylinder, and its volume cannot be calculated using the circular cylinder formula. Our calculator supports calculations specifically for a circular cylinder.

How to find the volume of a hollow cylinder if given the height, external diameter, and internal diameter?

To find the volume of a hollow cylinder, first determine the external and internal radii by dividing each diameter by two. Then, apply the formula:

$V = \pi h (r_1^2 - r_2^2)$

In this case, $r_1$ is the external radius, and $r_2$ is the internal radius. Substitute the values to solve for the volume.

Can the calculator handle both metric and imperial units?

Yes, the calculator is equipped to accept inputs in both metric (e.g., meters, centimeters) and imperial (e.g., inches, feet) systems, providing flexibility and ease of use according to the user’s needs.

What is the difference between an oblique and right cylinder volume calculation?

The volume calculation for both oblique and right cylinders is the same ($V = \pi r^2 h$) because the volume is based on the base area and height, independent of the side’s inclination.

How do you find the radius of a cylinder if you have the volume and height?

To find the radius of a cylinder when given the volume and height, rearrange the cylinder volume formula ($V = \pi r^2 h$):

1. Solve for $r^2$:

   $r^2 = \frac{V}{\pi h}$

2. Take the square root of both sides to solve for $r$:

   $r = \sqrt{\frac{V}{\pi h}}$

Example: Find the radius of a cylinder with a volume of 314.159 cubic meters and a height of 10 meters.

$r^2 = \frac{314.159}{\pi \times 10} = \frac{314.159}{31.4159} \approx 10$

$r = \sqrt{10} \approx 3.16 \text{ meters}$

By utilizing the cylinder volume calculator, users can ensure accurate and easy computation of volume for diverse cylindrical shapes across various applications, making it an essential tool for both educational and professional purposes.