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

## Example Questions

### Example Question #51 : How To Find The Volume Of A Prism

Find the volume of the prism.

Explanation:

Recall how to find the volume of any prism.

Since the base is a trapezoid, recall how to find the area of a trapezoid.

Plug in the given bases and height to find the area of the trapezoid.

Now, plug this in to find the volume of the prism.

### Example Question #52 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Explanation:

Recall the formula to find the volume of any prism:

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

Plug in the given side to find the area of the base.

Next, plug in the area of the base and the height to find the volume of the prism.

Remember to round to  places after the decimal.

### Example Question #53 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Explanation:

Recall the formula to find the volume of any prism:

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

Plug in the given side to find the area of the base.

Next, plug in the area of the base and the height to find the volume of the prism.

Remember to round to  places after the decimal.

### Example Question #54 : How To Find The Volume Of A Prism

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 : How To Find The Volume Of A Prism

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 : How To Find The Volume Of A Prism

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 #81 : Prisms

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 #82 : Prisms

A cylinder is cut in half and placed on top of a rectangular prism.

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 #83 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base 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 volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #84 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base 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 volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.