# Intermediate Geometry : How to find the volume of a cylinder

## Example Questions

### Example Question #31 : How To Find The Volume Of A Cylinder

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

Now, use the given radius and height to find the volume of the larger cylinder.

Next, use the given radius and height to find the volume of the smaller cylinder.

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

Make sure to round to  places after the decimal.

### Example Question #51 : Cylinders

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

Now, use the given radius and height to find the volume of the larger cylinder.

Next, use the given radius and height to find the volume of the smaller cylinder.

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

Make sure to round to  places after the decimal.

### Example Question #52 : Cylinders

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

Now, use the given radius and height to find the volume of the larger cylinder.

Next, use the given radius and height to find the volume of the smaller cylinder.

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

Make sure to round to  places after the decimal.

### Example Question #53 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

Then, recall how to find the volume of a cylinder:

, where  is the radius and  is the height.

Divide the volume by  to find the volume of the half cylinder.

Next, recall how to find the volume of a rectangular prism.

Plug in the given values to find the volume of the rectangular prism.

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

Remember to round to  places after the decimal.

### Example Question #54 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

Then, recall how to find the volume of a cylinder:

, where  is the radius and  is the height.

Divide the volume by  to find the volume of the half cylinder.

Next, recall how to find the volume of a rectangular prism.

Plug in the given values to find the volume of the rectangular prism.

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

Remember to round to  places after the decimal.

### Example Question #55 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

Then, recall how to find the volume of a cylinder:

, where  is the radius and  is the height.

Divide the volume by  to find the volume of the half cylinder.

Next, recall how to find the volume of a rectangular prism.

Plug in the given values to find the volume of the rectangular prism.

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

Remember to round to  places after the decimal.

### Example Question #56 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

Then, recall how to find the volume of a cylinder:

, where  is the radius and  is the height.

Divide the volume by  to find the volume of the half cylinder.

Next, recall how to find the volume of a rectangular prism.

Plug in the given values to find the volume of the rectangular prism.

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

Remember to round to  places after the decimal.

### Example Question #57 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

Then, recall how to find the volume of a cylinder:

, where  is the radius and  is the height.

Divide the volume by  to find the volume of the half cylinder.

Next, recall how to find the volume of a rectangular prism.

Plug in the given values to find the volume of the rectangular prism.

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

Remember to round to  places after the decimal.

### Example Question #58 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

Then, recall how to find the volume of a cylinder:

, where  is the radius and  is the height.

Divide the volume by  to find the volume of the half cylinder.

Next, recall how to find the volume of a rectangular prism.

Plug in the given values to find the volume of the rectangular prism.

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

Remember to round to  places after the decimal.

### Example Question #59 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

Then, recall how to find the volume of a cylinder:

, where  is the radius and  is the height.

Divide the volume by  to find the volume of the half cylinder.

Next, recall how to find the volume of a rectangular prism.

Plug in the given values to find the volume of the rectangular prism.

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

Remember to round to  places after the decimal.