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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.