1. Remember these!? Surface Area of a Prism = ph +2B
Volume of a Prism = Bh
Surface Area of a Cylinder = 2r2 +2rh
Volume of a Cylinder = r2h

2. Surface Area and Volume of Similar Figures
Geometry
Unit 11, Day 10
Ms. Reed

3. Rectangular Prism
With a partner, pick a length, width and height for your rectangular prism.
Find the Surface Area and Volume.
Pick a Scale Factor for the sides of your rectangular prism. (See Table 3)
Find the new sides.
Calculate the Surface Area and Volume
Repeat until you 3 scale factors are complete.

4. Table 4: Using the data from Table 3, complete Table 4!
With your partner, talk about what you notice.

5. What we discovered:
If the similarity ratio of two similar solids is a:b, then
The ratio of corresponding surface areas is a2:b2
The ratio of corresponding volumes is a3:b3
This applies to all similar solids, not just similar rectangular prisms.

6. Example 1
The surface are of two similar cylinders are 196in2 and 324in2. The volume of the smaller cylinder is 686in3. What is the volume of the larger cylinder?
First, find the similarity ratio of the sides!

7. Example 1: 196 324 REDUCE! 49 81 Find the square root
196 324
REDUCE!
49 81
Find the square root
7 is the similarity ratio of the sides 9

8. Example 1:
Now, create the similarity ratio of the sides into the similarity ratio of the volumes =
Now, set up a new proportion

9. Example 1:
686 = x
x = 1458

10. Example 2:
The surface area of two similar solids are 160 m2 and 250 m2. The volume of the larger one is 250 m3. What is the volume of the smaller one?
V = 128 m3

11. Homework
Work Packet: Surface Area and Volume of Similar Figures.