Ratios-Surface Areas and Volumes
Name ________________
A rectangular prism has six rectangular faces. The two rectangular prisms below are similar
figures.
D
E
6 units
9 units
3 units
10 units
15 units
5 units
1.
What is the scale factor of the edges of the prisms?
2.
Compute the surface area (sum of the area of all faces) of each rectangular prism.
Surface area of prism D ___________ units2 (square units)
Surface area of prism E ___________ units2 (square units)
3.
What is the scale factor of the surface areas of the prisms?
7012 b Scaling Lesson Student sheet Ratios/Surface Areas and Volume
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4.
How does this scale factor compare with the scale factor of the edges?
Check with your teacher before going to number 5.
5.
Explain why you think the relationship that you found in question 4 is true.
6.
How do you think the scale factor of the two volumes will compare with the scale factor
of the edges?
7.
Confirm your conjecture by finding the scale factors of the volumes.
Volume of prism D _________ units3 (cubic units)
Volume of prism E _________ units3 (cubic units)
Scale factor __________
8.
How does this scale factor compare with the scale factor of the edges?
9.
Explain why you think the relationship that you found in question 8 is true.
Check with your teacher before going to number 10.
10.
Summarize your conclusions, including your discoveries about the relationships
between the scale factors of the edges, perimeters, areas, surface areas, and volumes.
7012 b Scaling Lesson Student sheet Ratios/Surface Areas and Volume
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