Volume of a Cylinder Calculator | Free Online Volume of a Cylinder Calculator with Steps - BYJUS

# Volume of a Cylinder Calculator

Volume of a cylinder calculator is a free online tool that helps us calculate the volume of a cylinder, as well as its radius, height and base area. Let us familiarize ourselves with using the calculator....Read MoreRead Less

### How to use the ‘volume of a cylinder calculator’?

Follow these steps to use the ‘volume of a cylinder calculator’:

Step 1: Enter the two known measures out of radius, height, base area, or volume, into the respective input boxes, and the unknown measures will be calculated.

Step 2: Select the appropriate unit for the inputs and outputs.

Step 3: You can also select the desired value of ‘pi’ from the dropdown box. The values can be the following; it is either 3.14, $$\pi$$, or $$\frac{22}{7}$$.

Step 4: Now, click on ‘Solve’ to obtain the result.

Step 5: Click on the ‘Show Steps’ button to view the solution to find the missing measures, in a stepwise format.

Step 6: Click on the   button to enter new inputs and start again.

Step 7: Click on the ‘Example’ button to play with random input values.

Step 8: When you click on the ‘Explore’ button you can see how the volume of the cylinder changes by changing the radius and height of the cylinder.

Step 9:  When on the ‘Explore’ page, click the ‘Calculate’ button if you want to go back to the calculator.

### What is the volume of a cylinder?

The volume of a cylinder is the amount of space occupied by the cylinder. If we take an example of a cylindrical tank, the amount of water that fills the tank to the brim represents the approximate volume of the cylindrical tank.

### Formulas used in the ‘volume of cylinder calculator’

When the radius r and height h of the cylinder are known, the volume V and base area B of the cylinder are calculated as:

Volume of cylinder, V = $$\pi r^2h$$

Base area of cylinder, B = $$\pi r^2$$

When the volume V, and base area B of the cylinder are known, the radius r and height h of the cylinder are calculated as:

Volume of cylinder, V = B$$\times$$h

Therefore, height of cylinder, h = $$\frac{V}{B}$$

Base area of cylinder B = $$\pi r^2$$

Therefore, radius of cylinder, r = $$\sqrt{\frac{B}{\pi}}$$

When the base area B and height h of the cylinder are known, the volume V and radius r of the cylinder are calculated as:

Volume of cylinder, V = B$$\times$$h

Radius of cylinder, r = $$\sqrt{\frac{B}{\pi}}$$

When the radius r and volume V of the cylinder are known, the height h and base area B of the cylinder are calculated as:

Volume of cylinder, V = $$\pi r^2$$h

Therefore, height of cylinder, h = $$\frac{V}{\pi r^2}$$

Base area of cylinder, B = $$\pi r^2$$

When the height hand volume V of the cylinder are known, the radius r and base area B of the cylinder are calculated as:

Volume of cylinder, V = $$\pi r^2h$$

Therefore, radius of cylinder, r = $$\sqrt{\frac{V}{\pi h}}$$

Base area of cylinder, B = $$\frac{V}{h}$$

### Solved Examples on Volume of a Cylinder Calculator

Example 1: Find the volume and base area of the cylinder of radius 7 cm and height of 15 cm. (Take $$\pi=\frac{22}{7}$$)

Solution:

Volume of a cylinder, V = $$\pi r^2h$$

= $$\frac{22}{7}\times7^2\times15$$

= 2310 $$cm^3$$

Base area, B = $$\pi r^2$$

= $$\frac{22}{7}\times7^2$$

= 154 $$cm^2$$

So, the volume of the cylinder is 2310 cubic centimeters and the base area is 154 square centimeters.

Example 2: Find the height and radius of the cylinder whose base area is 54 square inches and the volume is 158 cubic inches. (Take $$\pi$$ = 3.14)

Solution:

Height of the cylinder, h = $$\frac{V}{B}$$

= $$\frac{158}{54}$$

= 2.926 inches

Radius of the cylinder, r = $$\sqrt{\frac{B}{\pi}}$$

= $$\sqrt{\frac{54}{3.14}}$$

= 4.147 inches

So, the height of the cylinder is 2.926 inches and the radius of the cylinder is 4.147 inches.

Example 3: Find the radius and base area of a cylinder whose volume is 154 cubic meters and height is 7 meters.(Take $$\pi=\frac{22}{7}$$)

Solution:

Radius of the cylinder, r = $$\sqrt{\frac{V}{\pi h}}$$

= $$\sqrt{\frac{154\times7}{22\times7}}$$

= $$\sqrt{7}$$

= 2.646

Base area of cylinder, B = $$\frac{V}{\pi h}$$

= $$\frac{154}{7}~m^2$$

= 22 $$m^2$$

So, the radius of the cylinder is 2.646 meters and the base area is 22 square meters.

Example 4: Find the height and base area of a cylinder whose radius is 14 centimeters and the volume is 380 cubic centimeters. (Take $$\pi=\frac{22}{7}$$)

Solution:

Base area of cylinder, B = $$\pi r^2$$

= $$\frac{22}{7}\times14^2$$

= 616 square centimeters

Height of cylinder, h = $$\frac{V}{\pi r^2}$$

= $$\frac{380\times7}{22\times14^2}$$

= 0.617 centimeters

So, the base area of the cylinder is 616 square centimeters and the height of the cylinder is 0.617 centimeters.

Example 5: Find the radius and volume of a cylinder whose height is 21 cm and the base area of a cylinder is 502 square centimeters. (Take $$\pi$$ = 3.14)

Solution:

Radius of cylinder, r = $$\sqrt{\frac{B}{\pi}}$$

= $$\sqrt{\frac{502}{3.14}}$$

= 12.644 cm

Volume of cylinder, V = B$$\times$$h

= 502$$\times$$21

= 10542 $$cm^3$$

So, the radius of the cylinder is 12.644 centimeters and the volume of the cylinder is 10542 cubic centimeters.

Frequently Asked Questions on Volume of a Cylinder Calculator

A cylinder has two circular bases and a curved surface. The faces do not meet. Hence, a cylinder does not have any vertices.
On the other hand, a cylinder has two edges where its curved surface and its circular bases meet.

The formula for curved or lateral surface area of a cylinder = 2πrh where, r is the radius of the cylinder and h is the height of the cylinder.

A cylinder has two circular bases.

A hollow cylinder is empty from the inside. Consider a hollow cylinder with an outer radius R, an inner radius r and height h.

Volume of hollow cylinder = πR2h – πr2h