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

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

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.

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

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.

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!

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

Example 1: Now, create the similarity ratio of the sides into the similarity ratio of the volumes 73 93 = 343 729 Now, set up a new proportion

Example 1: 686 = 343 x 729 x = 1458

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

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