Math is used everyday especially in the realms of engineering and construction. Imagine that you have decided to build a swimming pool. You have some requirements for the pool, and need to know how much it is going to cost. You can use math to answer your questions.

Part 1: Calculating the design for the pool.

Question 1: Pools are either measured in yards or meters. How many feet are in a yard? About how many feet are in a meter? (Round your answer to the nearest tenth of a foot.) Which is longer, a yard or a meter?

The design for the pool is:

- It should be rectangular, 25 meters long and 15 meters wide.
- The bottom of the first five meters of the pool is flat and is 1 meter deep.
- In the next 10 meters, the pool gets deeper at a rate of 1 meter of depth for every two meters of length, so that at 15 meters from the shallow end of the pool, the pool is 6 meters deep.
- The last 10 meters of the pool also have a flat bottom, and are 6 meters deep.

Use the information above to figure out the next questions. Questions 2 - 7 will help you answer later questions:

Question 2: What is the area of the surface of the pool?

Question 3: What is the area of the wall at the shallow end of the pool?

Question 4: What is the area of the wall at the deep end of the pool?

Question 5: What is the area of one of the sides of the pool? (break up larger shape into easier shapes)

Question 6: What is the area of the bottom of the pool?

Question 7: How many cubic meters of water are you going to need to fill the pool? (In other words, what is the volume of the pool?)

(Hint: Use the areas you just figured out to answer this question.)

Question 8: You have picked out a two different tiles that you could use to cover the bottom and sides of the pool.

a. The blue tile is 25 centimeters on a side. How many of them does it take to cover a square meter?

b. Each red tile costs $2.75 but the store is currently offering a 15% off sale

Question 9: How many tiles (of each color) will it take to cover the sides and bottom of the pool?

Question 10: Which tile would be the most economical to use and how much will it cost to cover the pool in tile?

a. Each blue tile costs $1.25.

b. Each red tile costs $2.75 but the store is currently offering a 15% off sale

Question 11: How many gallons of water will our pool hold? (Hint: The metric system unit for volume is the liter. It takes 1000 liters to fill a cubic meter with water. There are about 4 liters in a gallon.)

Question 12: There are 3 ways to fill your pool, 2 local pool water supply companies that will deliver water to fill your pool and to use your hose. Which is the most cost effective?

a. Company A’s trucks hold 9000 gallons of water and will cost $500 but they are currently having a 5% sale.

b. Company B’s trucks hold 6000 gallons of water and will cost $350

c. It will cost you approximately $0.002 per gallon to fill the pool with your hose.

Question 13: What will be the final cost to purchase the tiles and fill your pool with water?

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