Slide 1 - Slide 1

Finding Volume

To find the volume of a solid prism, simply take the area of the base and multiply it by how high the base has been “stacked up.” In other words, multiply the area of the base by how high the prism is. This works for any prism, no matter the shape of the base! Even cylinders!

Image description:
There are three columns.
In column one: A triangular prism sliced into triangular sections. A slice of cheese in the shape of a triangular prism, sliced into triangular sections.
In column two: A rectangular prism sliced into rectangular sections. A stack of dollar bills, and each bill is in the shape of a rectangle.
In column three: A cylinder sliced into circles. A cucumber sliced into circles.

 

Slide 2

The volume formula for any prism is:
The volume equals the area of the base times the height of the prism.
Volume equals the area of the base times the height.
Click Step 1 and Step 2 to show the example.

Image Description:
A table with 3 columns.
In column one, labeled Triangular Prism: A triangular prism with triangle base whose base is a right triangle with legs measuring three inches and four inches and the hypotenuse measures five inches. The height of the prism is eight inches.
In column two, labeled Step 1: Volume = Base times height. The base is a triangle. So, we will need the area of a triangle formula. Base equals Area of a triangle equals ½ base times height of a triangle.
In column 3, labeled Step 2: Volume = Base times height; Volume equals open parenthesis, ½ times height of a triangle, close parenthesis, times height of a prism; Volume equals open parenthesis, ½ times 4 inches times 3 inches, close parenthesis, times 8 inches; Volume equals 48 square inches.

 

Slide 3

The volume formula for any cylinder is:
The volume equals the area of the base times the height of the cylinder.
Volume equals the area of the base times the height.
Click Step 1 and Step 2 to show the example.

Image Description:
A table with three columns.
In column one, labeled Cylinder, A cylinder whose base is a circle with radius of two and five-tenths feet. The cylinder has a height of six and twenty-four hundredths feet.
In column two, labeled Step 1, Volume = Base times height. The base is a circle. So, we will need the area of a circle formula. Base equals Area of a circle equals pi times radius squared.
In column three, labeled Step 2, Volume = Base times height; Volume equals, open parenthesis, pi times radius squared, close parenthesis, times the height of a prism; Volume equals, open parenthesis, pi times 2 times 5 squared, close parenthesis, times 6.24; Volume equals approximately 122.5221 square feet

 

Slide 4

To help plan how a piece of sculpture “interacts” with its setting, a sculptor will want to know the volume of the artwork. Let’s assume a sculptor is creating the prisms below. Use the formula to find the volume of these prisms. Type your answers in the blanks.

Image Description:

  1. A rectangular prism measuring four feet by 1 and eight-tenths feet by thirty-two feet.
  1. A triangular prism with a height of five and twenty-five hundredths feet, and the base triangle having a base length of two and six-tenths feet and a height of one and eight-tenths feet.

 

The correct answers are:

  1. 230.4 square feet
  2. 12.285 square feet

Slide 5

Sculptors may also use pyramids and cones as part of a sculpture. You can see the formulas below that they use to calculate volume for these solids.

For pyramids, the volume equals one-third the area of the base times the height. Where V is the volume, B is the area of the base, and h is the height of the prism.

Image Description: A pyramid with the Base and height labeled.

For cones, the volume equals one-third the area of the base or the volume equals one-third pi r squared times the height. Where V is the volume, B is the area of the base (or B equals pi r squared), r is the radius of the base, and h is the height of the prism.

Image Description: A cone with the Base and height labeled.

 


Slide 6

Here is an example of how to find the volume of a pyramid.
Click each step to see how to find the volume.

Image Description:
A square pyramid with a height of eight inches and whose base edges are four inches long.

A table with two columns and three rows.
Row 1: Step 1: Volume equals one-third times the area of the base times the height. Volume equals one-third times the length of the side squared times the height of the prism.
Row 2: Step 2: Volume equals one-third times four squared times eight
Row 3: Step 3: Volume equals forty-two and sixty-six hundredths square inches

 

Slide 7

Here is an example of how to find the volume of a cone.
Click each step to see how to find the volume.

Image Description:
A cone with a height of six and twenty-four hundredths feet and a radius of two and five tenths feet.

A table with two columns and three rows.
Row 1: Step 1: Volume equals one-third times the area of the base times the height. Volume equals one-third times pi times the radius squared times the height of the prism.
Row 2: Step 2: Volume equals one-third times pi times 2.5 squared times 6.24.
Row 3: Step 3: Volume equals thirteen pi square feet. The volume is approximately 40.8407 square feet.

 

Slide 8

Use the formula volume equals one-third the area of the base times the height to find the volume of these solids.

Image Description:

  1. A triangular pyramid with a height of four feet, and the triangle base has a base length of two and five-tenths feet and a height of two and seventeen hundredths feet.
  2. A cone with a height of twenty-four inches and a radius of eleven inches.

The correct answers are:

  1. 3.613 square feet
  2. 3041.06 square inches.

 

Slide 9

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