# How to find the Volume of a Cylinder in 4 Easy Steps

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### Key Points about Volume of a Cylinder

• The volume of a cylinder is the amount of space occupied by a cylinder, a three-dimensional shape with a circular base and straight sides that are perpendicular to the base.
• The formula for the volume of a cylinder is πr²h, where r is the radius of the circular base and h is the height of the cylinder.
• The volume of a cylinder can be calculated using a simple formula that takes into account the height and radius of the cylinder.

## The Short Explanation for Finding the Volume of a Cylinder

Finding Volume of a Cylinder can be completed easily by using the formula and following correct order of operations. The first step in finding Volume of a Cylinder is understanding that you are multiplying the area of the base by the height of the cylinder. The base happens to be a circle so you must use the Area of a Circle formula to calculate the area of the base. Be sure to remember that the radius is equal to half of the diameter. Once you know the area of the base, you must multiply it by the height of the cylinder. The final step for finding Volume of a Cylinder is to follow order of operations and simplify the equation.

The volume of a cylinder is a fundamental concept in geometry and mathematics. It is the amount of space occupied by a cylinder, a three-dimensional shape with a circular base and straight sides that are perpendicular to the base. The volume of a cylinder can be calculated using a simple formula that takes into account the height and radius of the cylinder.

The formula for the volume of a cylinder is πr²h, where r is the radius of the circular base and h is the height of the cylinder. This formula is derived from the fact that the volume of a cylinder is equal to the area of the base multiplied by the height. The base of a cylinder is a circle, and the area of a circle is given by πr², where r is the radius. Multiplying this area by the height of the cylinder gives the volume of the cylinder.

Common Core Standard: 8.G.C
Basic Topics:
Related Topics: Pythagorean Theorem, Parallel Lines Cut by a Transversal, Triangle Angle Sum, Exterior Angle of a Triangle, Volume of a Cone, Volume of a Sphere ## Volume of a Cylinder Formula: How to Use

The formula for calculating the volume of a cylinder is an essential concept in mathematics and engineering. It allows us to determine the amount of space occupied by a cylinder, which is a three-dimensional geometric shape with a circular base and straight sides. The formula for the volume of a cylinder is:

``````V = πr^2h
``````

where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder. The value of π is approximately equal to 3.14159.

### Calculating the Volume of a Cylinder

To calculate the volume of a cylinder, you need to know the values of the radius and height. If you have the diameter of the circular base instead of the radius, you can calculate the radius by dividing the diameter by 2.

Once you have the values of the radius and height, you can use the formula to find the volume of the cylinder. Here’s an example:

Suppose you have a cylinder with a radius of 5 cm and a height of 10 cm. To find the volume of the cylinder, you can use the formula as follows:

``````V = πr^2h
V = π(5 cm)^2(10 cm)
V = π(25 cm^2)(10 cm)
V = 250π cm^3
``````

Therefore, the volume of the cylinder is 250π cubic centimeters.

In summary, the formula for the volume of a cylinder is V = πr^2h, where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder. To calculate the volume of a cylinder, you need to know the values of the radius and height, and then plug them into the formula.

## Volume of a Cylinder with Diameter

To calculate the volume of a cylinder with diameter, one needs to know the diameter and height of the cylinder. The formula for the volume of a cylinder with diameter is:

``````V = π × (d/2)² × h
``````

Where `V` is the volume, `d` is the diameter, and `h` is the height of the cylinder.

It is important to note that the diameter is twice the radius of the cylinder. Therefore, if the radius is known, the diameter can be calculated by multiplying the radius by 2.

One can also use the diameter to calculate the radius of the cylinder. The formula for the radius of a cylinder with diameter is:

``````r = d/2
``````

Where `r` is the radius and `d` is the diameter of the cylinder.

Once the radius is known, one can calculate the volume of the cylinder using the formula for the volume of a cylinder with radius. The formula for the volume of a cylinder with radius is:

``````V = π × r² × h
``````

Where `V` is the volume, `r` is the radius, and `h` is the height of the cylinder.

In conclusion, calculating the volume of a cylinder with diameter is easy once the diameter and height are known. One can use the formula `V = π × (d/2)² × h` or convert the diameter to radius and use the formula `V = π × r² × h`.

## 3 Simple Volume of a Cylinder Examples

Calculating the volume of a cylinder is a crucial skill for anyone working in construction, engineering, or manufacturing.

1. In order to solve for Volume of a Cylinder you must know that the volume is equal to the base times the height.
2. The base is equal to a circle so you use the area of a circle formula to find the area of the base.
3. The height is equal to how tall the cylinder is.
4. You substitute in the radius of the cylinder for r, and the height of the cylinder for h.
5. Multiply everything together in your calculator being sure to use the correct units.

Here are a few examples that demonstrate how the volume of a cylinder is calculated.

### Example 1

Suppose a cylinder has a height of 10 cm and a radius of 6 cm. To calculate the volume of this cylinder, we can use the formula:

``````V = πr^2h
``````

where `V` is the volume, `r` is the radius, and `h` is the height. Plugging in the values, we get:

``````V = π(6 cm)^2(10 cm)
V = 1130.97 cm^3
``````

Therefore, the volume of the cylinder is approximately 1130.97 cubic centimeters.

### Example 2

Suppose a cylindrical tank has a diameter of 10 meters and a height of 15 meters. To calculate the volume of this cylinder, we need to first calculate the radius, which is half the diameter:

``````r = d/2
r = 10 m/2
r = 5 m
``````

Now that we know the radius, we can use the formula to calculate the volume:

``````V = πr^2h
V = π(5 m)^2(15 m)
V = 1178.1 m^3
``````

Therefore, the volume of the cylindrical tank is approximately 1178.1 cubic meters.

### Example 3

Suppose a cylindrical pipe has an outer diameter of 8 inches and an inner diameter of 6 inches. The height of the pipe is 12 inches. To calculate the volume of the pipe, we need to first calculate the radius of both the outer and inner circles:

``````r_outer = d_outer/2
r_outer = 8 in/2
r_outer = 4 in

r_inner = d_inner/2
r_inner = 6 in/2
r_inner = 3 in
``````

Now that we know the radii, we can use the formula to calculate the volume of the pipe:

``````V = π(r_outer^2 - r_inner^2)h
V = π((4 in)^2 - (3 in)^2)(12 in)
V = 113.1 in^3
``````

Therefore, the volume of the cylindrical pipe is approximately 113.1 cubic inches.

These examples demonstrate how the volume of a cylinder can be calculated using the formula `V = πr^2h`. By plugging in the values for the radius and height, anyone can calculate the volume of a cylinder quickly and easily.

## 5 Quick Volume of a Cylinder Practice Problems

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Volume of a Cylinder Quiz

Click Start to begin the practice quiz!

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Find the volume of the cylinder. 2 / 5

Find the volume of the cylinder. 3 / 5

Find the volume of the cylinder. 4 / 5

Find the volume of the cylinder. 5 / 5

Find the volume of the cylinder. 0%

## Volume of a Cylinder Equation with Radius

The volume of a cylinder is the amount of space inside the cylinder. It is measured in cubic units. The formula for calculating the volume of a cylinder is:

``````V = πr²h
``````

where `V` is the volume, `r` is the radius of the cylinder, and `h` is the height of the cylinder.

This formula can be derived by imagining the cylinder as a series of circular disks stacked on top of each other. The area of each disk is `πr²`, and the height of each disk is `h`. The volume of the cylinder is then the sum of the volumes of all the disks, which is `πr²h`.

It is important to note that the radius and height of the cylinder must be measured in the same units for the formula to work correctly. For example, if the radius is measured in centimeters, then the height must also be measured in centimeters.

The volume of a cylinder can be calculated using different units of measurement. For example, if the radius is measured in meters and the height is measured in centimeters, then the volume will be in cubic meters. In such cases, it is important to convert the measurements to the same units before applying the formula.

In summary, the formula for the volume of a cylinder is `V = πr²h`. It is based on the area of a circular disk and the height of the cylinder. The formula can be used with different units of measurement as long as the radius and height are measured in the same units.

## How to Find the Volume of a Cylinder FAQ

### How would you calculate the volume of a cylinder?

To calculate the volume of a cylinder, you would need to know the radius of the base and the height of the cylinder. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.

### What are all the formulas for volume of cylinder?

There is only one formula for the volume of a cylinder, which is V = πr²h.

### How much is multiplied to the volume of a cylinder?

There is no specific value that is multiplied to the volume of a cylinder. The volume of a cylinder is calculated using the formula V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.

### What is the formula for calculating the volume of a cylinder?

The formula for calculating the volume of a cylinder is V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.

### How to calculate volume of a cylinder with diameter and height?

To calculate the volume of a cylinder with diameter and height, you would need to first find the radius of the base. The radius can be found by dividing the diameter by 2. Once you have the radius, you can use the formula V = πr²h to calculate the volume of the cylinder.

### What is meant by the volume of a cylinder?

The volume of a cylinder is the amount of space inside the cylinder. It is measured in cubic units, such as cubic centimeters or cubic meters.

### How do you find the volume of a cylinder without the height?

It is not possible to find the volume of a cylinder without the height. The height is a necessary component in the formula for calculating the volume of a cylinder.

### Is 2/3 the volume of a cylinder?

No, 2/3 is not the volume of a cylinder. The volume of a cylinder is calculated using the formula V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.

## Volume of a Cylinder Worksheet: Video Explanation

Watch our free video on How to find the Volume of a Cylinder. This video shows how to solve problems that are on our free Volume of Cylinder worksheet that you can get by submitting your email above.

Watch the free How to find the Volume of a Cylinder video on YouTube here: How to find the Volume of a Cylinder

Video Transcript:

This video is about how to find volume of a cylinder and we’re going to use our volume of a cylinder practice worksheet with answers in order to show you how to do that.

Here we are at the first problem on our volume of cylinder worksheet 8th grade. In order to find the volume of a cylinder you have to find the area of the base and multiply it times the height of the cylinder. In terms of our cylinder here in order to find the area of the base the base is in the shape of a circle.

So in order to find the area of the base you have to use the area of a circle formula which is PI R squared. That’s the area of the base and then you have to multiply that times the height and in the case of this example or really all examples the height is always just the height of the cylinder.

We’ll just call it H so our formula for volume cylinder is the area of the base which in this case is a circle multiplied times the height. In order to simplify this what you’re going to do is you’re going to find the radius which is R and you’re going to find the height which is H. In terms of the radius all you have to do is look at our circle and our sphere here is labeled that’s our radius and our radius is seven inches.

We know that the radius is seven and then our height which is here is 11. We know our height is 11 inches so in order to solve this what you’re going to do is substitute in R or seven for radius and 11 for height and then you’re going to simplify. Volume will be pi times the radius which is seven squared times the height which is 11. The final step is to simplify. You will do pi times 7 squared times 11 which is 1690 3.32 inches because that’s our unit cubed and that’s our answer.

Moving onto the next volume of a cylinder problems on how to find the volume of a cylinder we are going to use our volume of a cylinder formula which we went over in the first problem. We know that volume is the area of the base which is PI R squared times the height. We already know the formula and we’re going to substitute in what they give us in this problem for the radius and for the height.

The easiest one in this example to substitute in for would be the height because the height is 35 inches. This is problem is helpful for learning how to find height of a cylinder. We already know the height the difference in this problem when it comes to the radius is that instead of giving us the radius they gave us the diameter.

This 17 inches refers to the whole diameter of the circle so in order to get the radius the radius is of course equal to 1/2 of the diameter. If the diameter is 17 inches the radius is going to be half of that which is 8 point 5. Now we know our radius and our height that we’re going to use the substitute into our formula  we know that we have to use pi then we have to use 8.5 for the radius squared and then we have to multiply that times 35 for the height.

When we substitute these in we substitute it in 8.5 in for R and then 35 in for the height then when you simplify our formula you will get seven thousand nine hundred and forty four point three inches cubed and that’s going to be your solution. Try all the practice problems by downloading the cylinder volume worksheet above.

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