JUMP TO TOPIC

# Volume of a Cylinder Calculator + Online Solver With Free Steps

The **Volume of a Cylinder Calculator** is used to compute the volume of a cylinder. It takes the **radius** and **height** of the cylinder as input and outputs the volume.

A cylinder is a symmetrically shaped object with straight **parallel sides** and a **circular** cross-sectional area. It is a **three-dimensional** figure with **two** equal **circular bases** joined by a curved surface. The two circular bases are placed at a distance which is referred to as the **height** of the cylinder.

The **radius** of the cylinder is the radius of the circular base. It is the distance from the **center** of the circular base to the **circumference** of the circle.

The **Volume** of a symmetrical body is given by:

**Volume = Base × Height **

The **base **of a cylinder is the area of the circle at the base of the cylinder. It is given by:

\[ \text {Area of Base of Cylinder } = π \ r^{2} \]

Where **r** is the radius of the circle at the base. The square of the radius is multiplied by pi **π** which is an irrational number. The **value** of π is given by:

\[ π = \frac{22}{7} = 3.14 \]

Putting the equation for “Base” in the **Volume** equation gives:

\[ \text{Volume} = π \ r^{2} × h \]

Where **h** is the height of the cylinder. It is the distance measured from the center of one circular base to the other circular base.

The calculator uses this **formula** to calculate the volume of the cylinder. It calculates the result up to **four **decimal places.

The volume is measured in units of **cubic** meters, cubic inches, or cubic centimeters.

## What Is a Volume of a Cylinder Calculator?

**The Volume of a Cylinder Calculator is an online tool that is used to determine the volume of the cylinder up to four decimal places by taking the radius and height of the cylinder as input.**

The volume of a cylinder tells how much a cylinder can store a liquid in it. It is the amount of **space** the material occupies.

The volume is also required especially when calculating the **density** of an object.

## How To Use the Volume of a Cylinder Calculator

The user can use the Volume of a Cylinder Calculator by following the steps given below.

### Step 1

The user must first enter the radius of the cylinder in the input tab of the calculator. It should be entered in the block labeled as **Radius**.

It is not necessary to specify the unit along with the value of radius.

The radius of a cylinder is always a **positive quantity**. If the user enters a negative value of radius in the calculator’s input tab, the calculator gives the signal **Not a possible cylinder**.

### Step 2

The user must now enter the height of the cylinder in the calculator’s input window. It should be entered against the block titled **Height**.

The **units** of radius and height should be the **same** for accurate results.

For example, if the radius of the cylinder is in **inches**, the height of the cylinder should also be in inches as entered by the user.

The height can also never be a negative entity. If a negative height is entered, the calculator will again prompt **Not a possible cylinder**.

### Step 3

The user must now press the **Submit** button for the calculator to process the radius and height of the cylinder. It starts computing the result after submitting the input and opens the output window.

### Output

The Output window of the Volume of a Cylinder Calculator consists of only one window which is given below:

#### Result

The calculator computes the **volume of the cylinder** and displays the result in this window. It calculates the volume by using the formula:

\[ \text{Volume} = π r^{2} × h \]

The calculator also provides all the **mathematical steps** to calculate the volume of the cylinder. The user can press Need a step-by-step solution to this problem? to view all the steps in detail.

Suppose the user enters the **radius** **r** as 2 inches and the **height ****h** of the cylinder as 3 inches. The calculator puts the values of r and h in the above formula and computes the **result** as follows:

\[ \text{Volume} = π (2)^{2} × (3) \]

\[ \text{Volume} = 12 π \]

Putting the value of **π** which is an irrational number as **3.1416** and computing the volume of the cylinder gives:

**Volume = 37.6991**

This volume is in units of **cubic inches**. Notice that both the radius and the height of the cylinder are in the same unit that is inches.

## Solved Examples

The following examples are solved through the Volume of a Cylinder Calculator.

### Example 1

Calculate the **volume **of a cylinder that has a **radius** of 5 meters and a **height** of 10 meters.

### Solution

The user must first enter the **radius** and **height** of the cylinder in the input window of the calculator. The radius and height are specified as:

**Radius = 5**

**Height = 10 **

Both the radius and height of the cylinder are in units of **meters**.

After entering the input data, the user must press the **Submit** button for the calculator to compute the volume of the cylinder.

The calculator opens the output window and displays the **Result** as follows:

**Volume of Cylinder = 250 π **

Putting the value of π as $ \dfrac{22}{7} $, the calculator also gives the volume as:

**Volume = 785.398 **

The unit for this volume is **cubic meters**. Therefore, the volume of the cylinder is 785.398 $ m^{3} $.

### Example 2

A cylinder has a **radius** of 3.5 feet and a **height** of 15 inches. What is the **volume** of the cylinder in cubic inches?

### Solution

The user must enter the radius and height of the cylinder in the calculator’s input window. Notice that the radius and height are not in the **same units**.

The user must first convert the radius into **inches** as the volume required should be cubic inches. The user must do this on his own for correct results as the calculator assumes the units of radius and height to be the **same**.

To convert **feet into inches**, we know that 1 foot = 12 inches.

Therefore:

**3.5 feet = 3.5 × 12 inches **

**3.5 feet = 42 inches **

So the **radius** of the cylinder in inches is **42 inches**.

The user must now place the values of **radius** and **height** of the cylinder in the calculator’s input tab as follows:

**Radius = 42 **

**Height = 15**

After entering the values, the user must now **Submit** the input data and let the calculator compute the volume.

The calculator shows the **Result** as follows:

**Volume of Cylinder = 26460 π **

Placing the value of **π**, the calculator displays the volume of the cylinder as follows:

**Volume = 83126.5**

Thus, the **volume** of the cylinder is 83126.5** cubic inches**.