Review Similar Triangles Ratio & Proportion Similar Triangles Word Problems Volume

100 points Solve for x. x = 12

200 points A 100 foot building casts a shadow of 140 feet. If there is an 80 foot building nearby, how long is it’s shadow? 112 feet

300 points Find the value of x. x = 6 8x + 8 2x

400 points Suppose the points B and C lie on. What is the length of if, and BD = 20? AC = 30

500 points An airplane has a wingspan of (x 2 – 4) ft and a length of (x 2 + 8) ft. A scale model of this plane has a wingspan of (x + 2) ft and a length of (x + 4) ft. Based on this information, use a proportion to find the wingspan of the actual airplane. 60 feet

100 points Find x. x = 5 x

200 points Find the value of y. y = 4 y + 5 y

300 points Solve for the variable given the ratio of two side lengths. x = 8 AB: BC = 5: 6 3x – 4 2x + 8 A B C

400 points Find the length of side XC if BC = 12. XC = 8 A B C D X 3 6

500 points Find x. x = 5 x

100 points The ratio of the birth weight to the adult weight of a male black bear is 5:900. The average birth weight is 20 oz. Find the average adult weight in pounds. 225 pounds

200 points Assume that a wheelchair ramp has a slope of. If a specific ramp has a run of 12 feet, what is it’s rise? 1.5 feet

300 points The volume of a rectangular pool is 4,608 cubic meters. Its length, width, and depth are in the ratio of 2: 9: 4. Find the number of meters in each of the three dimensions of the pool. 8m, 36m, 16m

400 points A rectangular cylinder with the dimensions 12 in by 17 in by 18 in is to be filled with water, using a cylindrical cup whose radius is 3 inches and whose height is 6 inches. What is the maximum number of full cups of water that can be placed into the container without the water overflowing the container? 21 cups

500 points Gulliver’s Travels was written by Jonathan Swift in In the story, Gulliver is shipwrecked and wanders ashore to the island of Lilliput. The average height of the people in Lilliput is 8 inches. a) If Gulliver is 7 feet tall, what is the ratio of his height to the average height of a Lilliputian? b) After leaving Lilliput, Gulliver visits the island of Brobdingnag. The ratio of the average height of these natives is proportional to the ratio of Gulliver’s height to the average height of a Lilliputian. What is the average height of a Brobdingnagian, in feet? 21: 2 and 73.5 ft

100 points Find the volume of the figure. V =

200 points Find the volume of the figure Round to the nearest tenth. V =

300 points The dimensions of a brick, in inches, are 3 by 2 by 3. How many such bricks are needed to have a total volume of exactly one cubic foot? 96 bricks

400 points Find x, to the nearest tenth, given that the volume is x = 3.7 x

500 points During a chemistry lab, you use a funnel to pour a solvent into a flask. The radius of the funnel is 4 centimeters and its height is 11 centimeters. If the solvent is being poured into the funnel at a rate of 95 milliliters per second and the solvent flows out of the funnel at a rate of 75 milliliters per second, how long will it take before the funnel overflows? Round your answer to the nearest tenth of a second. 9.2 seconds