To honor Benjamin Franklin, designers will place a statue of him outside the entrance to the Liberty Bell exhibit hall in Philadelphia. The designers decide to place a smaller, similar version on a table inside the building. The dimensions of the life-sized statue will be four times those of the smaller statue. Planners expect to need 1.5 pints of paint to coat the small statue. They also know that the small statue will weigh 14 pounds. a. How many gallons of paint are needed to paint the life-sized statue? Scale factor = 4 Surface Area ratio = 4 2 = 16 Paint needed = 16(1.5) = 24 pints = 3 gallons b. If the small statue is made of the same material as the enlarged statue, how much will the life-sized statue weigh? Scale factor = 4 Volume ratio = 4 3 = 64 Weight of life sized statue = 64(14) = 896 pounds

Ratios of Similarity May 11, 2016

Objectives 0 CO: SWBAT use similarity to help them find volumes and surface areas. 0 LO: SWBAT explain to a partner when to cube something.

The Blackbird Oil Company is considering the purchase of 20 new oil storage tanks. They can buy jumbo storage tanks or standard models. Each standard model holds 12,000 gallons. Its dimensions are 4/5 the size of the similarly shaped jumbo model. a. How much more storage capacity would the 20 jumbo models give Blackbird Oil over standard models? Volume Ratio: (5/4) 3 = 125/64 Volume of Jumbo = (125/64)(12,000) = 23,437.5 Difference between Jumbo and Standard = 23,437.5 – 12,000 = 11, Jumbos = 20(11, 437.5) = 228,750 more b. If jumbo tanks cost 50% more than standard tanks, which tank is a better buy? Jumbo because they hold almost twice as much for only 1.5 times the cost. c. If 1 cubic foot is approximately 7.48 gallons, what is the volume of the standard model storage tank in cubic feet? 12,000/7.48 = 1,604.3 cubic feet d. One meter is approximately 3.28 feet. How many cubic meters of oil does the standard model storage tank hold? 1,604.3/(3.28) 3 = 45.5 cubic meters e. What was different about your calculation in part (d) compared to part (c)? How is this related to the scale factors for similar solids? In part (c), gallons is a measurement of volume, so it can be used as the conversion factor. In part (d), the conversion ratio must be cubed because the given conversion is for linear units, not cubic units.

Rosilaine is ordering wood chips to cover her dog run area. The size of the dog run is 9.5 feet by 12 feet and she wants the wood chips to be 4 inches deep. The wood chips are sold by the cubic yard at the landscaping supply store. Rosilaine calculates that she should order 12 cubic yards of wood chips, but when she calls to place her order, the person at the landscaping supply store tells her that 12 cubic yards of wood chips would fill an entire dump truck! That sounds like a lot, and she worries that she has made a mistake. Can you help her? Check Rosilaine’s calculations and explain her probable error. Then suggest to Rosilaine how many cubic yards of wood chips she should order so that she will have enough but will not have too much left over. Show your calculations with units. 0 4 inches = 1/3 foot 0 V = (9.5)(12)(1/3) = 38 ft /(3 3 ) = 1.4 yd 3 0 She probably divided by 3 instead of 27.