Volume of a Cylinder Calculator - Find a Cylinder Volume

Our volume of a cylinder calculator enables you to calculate the volume of a cylinder using its diameter or radius. This calculator allows you to find the volume of a Right or Oblique Full cylinder and a Hollow cylinder.

Do you know how to find the volume of a cylinder? Understanding how to calculate the volume of a cylinder is an important skill in math, with many practical applications. For example, if you want to figure out how much water fits in a cup, or how much coffee in your favorite mug, you'll need to know its volume.

How to Calculate Volume of a Cylinder?

A cylinder is a three-dimensional solid that has two parallel circular bases and a curved surface that connects them. It resembles a can or a drum. To calculate the volume of a cylinder, we need to know two parameters – the radius (or diameter) and height:

cylinder volume = π × cylinder radius2 × cylinder height

The cylinder volume calculator helps in finding the volume of right, hollow, and oblique cylinders.

Volume of a Hollow Cylinder

A hollow cylinder, also known as a cylindrical shell, is a three-dimensional region bounded by two right circular cylinders with the same axis and two parallel annular bases perpendicular to the cylinders' common axis. It's easier to understand by imagining a pipe or a hollow tube – the hollow cylinder is the material that makes up the pipe.

The formula for the volume of a hollow cylinder is:

cylinder_volume = π × (R2 - r2) × cylinder_height

where R – external radius, and r – internal radius

Similarly, we can calculate the cylinder volume using the external diameter, D, and internal diameter, d, of a hollow cylinder with this formula:

cylinder_volume = π × [(D2 - d2)/4] × cylinder_height

To calculate the volume of a cylindrical shell, let's consider the example of a bamboo pole:

1. Enter the external diameter of the cylinder. Let's assume it's 10 cm.
2. Determine the internal cylinder diameter. Assume it's 8 cm.
3. Find out what's the height of the cylinder; let's say it's 5 meters or 500 cm.
4. Using the formula, the volume of this hollow cylinder is equal to 14137.17 cm³.

Remember that the result is the volume of the material itself. If you want to calculate the volume of the hollow space inside the bamboo pole, use the standard formula for the volume of a cylinder – the calculator will calculate it in the blink of an eye!

Volume of an Oblique Cylinder

An oblique cylinder is one where the sides are not perpendicular to the bases, in contrast to a standard 'right cylinder'. How to calculate the volume of an oblique cylinder? The formula is the same as for the straight one. Just remember that the height must be perpendicular to the bases.

FAQs

How do you draw a cylinder?

To sketch a cylinder, follow these steps:

1. Draw a slightly elongated oval shape. The more elongated it is, the closer you are to viewing the cylinder from the side.
2. Draw two equal, parallel lines extending downward from the far ends of the oval.
3. Connect the bottom ends of the two lines with a curved line that mirrors the bottom half of the oval shape you drew initially.
4. Add shading and shadows as desired to enhance the three-dimensional effect.

How do you calculate the weight of a cylinder?

To calculate the weight of a cylinder:

1. Find the square of the cylinder's radius.
2. Multiply the squared radius by pi and the cylinder's height.
3. Multiply the resulting volume by the density of the cylinder's material. The result is the cylinder's weight.

How do you calculate the surface area to volume ratio of a cylinder?

1. Calculate the volume of the cylinder using the formula πr2h.
2. Calculate the surface area of the cylinder using the formula 2πrh + 2πr2.
3. Express the volume and surface area as a ratio, i.e., πr2h : 2πrh + 2πr2.
4. Alternatively, simplify the ratio to rh : 2(h+r).
5. Divide both sides of the ratio by one of the terms to obtain the simplest form.

How do you find the height of a cylinder?

If you know the volume and radius of the cylinder:

1. Ensure the volume and radius are in the same units (e.g., cm³ and cm).
2. Square the radius.
3. Divide the volume by the squared radius and pi to obtain the height in the same units as the radius.

If you know the surface area and radius (r):

1. Ensure the surface area and radius are in the same units.
2. Subtract 2πr² from the surface area.
3. Divide the result of step 2 by 2πr.
4. The result is the height of the cylinder.

How do you find the radius of a cylinder?

If you know the volume and height of the cylinder:

1. Ensure the volume and height are in the same units (e.g., cm³ and cm).
2. Divide the volume by pi and the height.
3. Take the square root of the result.

If you know the surface area and height (h):

1. Substitute the height, h, and surface area into the equation: surface area = 2πrh + 2πr².
2. Divide both sides of the equation by 2π.
3. Subtract surface area/2π from both sides.
4. Solve the resulting quadratic equation.
5. The positive root is the radius.

How do you find the volume of an elliptical cylinder?

To find the volume of an elliptical cylinder:

1. Multiply the smallest radius of the ellipse (minor axis) by its largest radius (major axis).
2. Multiply this product by pi.
3. Divide the result of step 2 by 4. The result is the area of the ellipse.
4. Multiply the area of the ellipse by the height of the cylinder.
5. The result is the volume of the elliptical cylinder.

How do you find the volume of an inclined cylinder?

To calculate the volume of an inclined cylinder:

1. Find the radius, side length, and slant angle of the cylinder.
2. Square the radius.
3. Multiply the squared radius by pi.
4. Calculate the sine of the angle.
5. Multiply the sine by the side length.
6. Multiply the results from steps 3 and 5 together.
7. The result is the volume of the inclined cylinder.

How do you calculate the swept volume of a cylinder?

To compute the swept volume of a cylinder:

1. Divide the bore diameter by 2 to get the bore radius.
2. Square the bore radius.
3. Multiply the squared radius by pi.
4. Multiply the result of step 3 by the length of the stroke. Ensure the units for bore and stroke length are consistent.
5. The result is the swept volume of one cylinder.