1. ΔABC ΔEDC. All measurements are in centimeters.

DE = , AG = , CF =

Step 1: Solve for DE using the fact that they are similar

triangles

Step 2: Identify the theorem needed to solve for AG

Step 3: Label AG as x. Setup a proportion based on the theorem identified in step 2 using 31.5, 63, 48, and x.

Step 4: Use either the same method used in step 3 to find CF or compare the two similar triangles and solve for CF.

  1. The right cylinders shown are similar. The surface area of the base small cylinder is 49π square inches. The surface area of the base of the large cylinder is 169π square inches. The volume of the large cylinder is 845π cubic inches. Find the volume of the small cylinder.

Volume = ______

Step 1: Identify the type of ratio you can setup given the info above and set it up in the chart below

Dist. Ratio / Area Ratio / Volume Ratio

Step 2: Find the ratio you need using the table above

Step 3: Setup a proportion where the volume of the small cylinder is

represented by the variable x.

Step 4: Solve for x

3. A scientist on twitter claims that he has grown the world’s largest apple. It has a diameter of 24 inches and weighs 55 pounds! With some research, you find that the average apple has a diameter of 2 inches and is only .75 pounds. Based off this information, do you think that an apple with a diameter of 24 inches would be roughly 55 pounds?

Dist. Ratio / Area Ratio / Volume Ratio

Step 1: Identify the type of ratio you can set up to the right

Step 2: Identify and solve for the ratio you need

Step 3: Let x represent the weight of the 24” diameter apple.

Solve for x and determine if it is reasonably close to 55 pounds

4. Volume = ______Step 1: Identify if the two triangles are similar with a similarity statement

Step 2: Identify which sides correspond for the similar triangles

Step 3: Set up one proportion for x and a second proportion for y and solve

5.On a blueprint, the scale indicates that 6 centimeters represents 25 feet. What is the area of the actual room that is 10.8 centimeters long and 9 centimeters wide on the blueprint?

Step 1: Identify the ratio of side lengths given the blueprint scale factor

Step 2: Set up a proportion to find the actual length the side of the room that is 10.8cm in the blueprint

Step 3: Set up a proportion to find the actual length the side of the room that is 9cm in the blueprint

Step 4: Use the converted dimensions in feet from steps 2 and 3 to calculate the actual area of the room (include units)

6. Matt wants to know how far he is from the space needle. He is standing 12 feet from a tree that is 18 feet tall. When he looks over the top of the tree, he can just see the top of the space needle. He knows that the space needle is 603 feet tall. His eyes are 5 feet 9 inches from the ground. How far is he from the space needle? Give your answer to the nearest half foot.

Step 1: Add a horizontal line from Matt’s eyes to the space needle. Identify the 2 similar triangles

Step 2: Sketch the 2 triangles below

Step 3: Label the lengths of the legs of the smaller triangle

(subtract Matt’s height from the height of the tree)

Step 4: Label the lengths of the legs of the larger triangle.

(Subtract Matt’s height from the height of the Space Needle)

Step 5: Set up a proportion comparing corresponding sides of the similar triangles and solve for the missing length

7. Solve the following proportions

a.b.

Step 1: Cross multiply (add parenthesis to the quantity x+5)

Step 2: Distribute 8 to both x and +5 and solve

Repeat for 4.b.