In this section, you will use an interactive applet to investigate how dilating a prism affects the volume of the dilated prism. You will also look for a relationship between the scale factor of the prism edge lengths and the scale factor of the volumes.

This activity might not be viewable on your mobile device.Interactive exercise. Assistance may be required. Click on the image to open an applet to investigate how using a scale factor affects the volume of similar rectangular prisms. Use the applet to complete the table below, and then use your table to answer the questions that follow.

Interactive popup. Assistance may be required.

Click here for directions to use the applet


Close Pop Up

Length l

Length L

Scale Factor
(L over T L I )

Volume of Prism B 

Volume of Prism A

(Scale Factor)3
(L over T L I )3

 Volume A over Volume B Volume A Volume B

1.73

3.46

2

1.73

13.86

8

8

1.73

2.60

1.5

 

 

 

 

1.73

5.20

 

 

 

 

 

1.73

1.39

 

 

 

 

 

1.73

0.87

 

 

 

 

 

Interactive popup. Assistance may be required.

Click to see an answer

Close Pop Up

What is the relationship between the scale factor and the ratio of the volumes?
Interactive popup. Assistance may be required.

Check Your Answer

The cube of the scale factor is equal to the ratio of Volume B to Volume A.Close Pop Up

If you know the volume of Prism B and the scale factor used to dilate Prism B into Prism A, how can you use that information to predict the volume of Prism A?
Interactive popup. Assistance may be required.

Hint

The scale factor relating the volumes is equal to the cube of the scale factor used to relate the edge lengths of the similar prisms.Close Pop Up
Interactive popup. Assistance may be required.

Check Your Answer

Multiply the volume of Prism B by the cube of the scale factor.Close Pop Up

Practice

Interactive exercise. Assistance may be required.