Volume 4.4

Warm Up: Find the volume of the shapes shown:

Outcome: M5 - Solve problems using SI and Imperial systems, that involve the surface area and volume of 3D objects including: right cones, right cylinders, right prisms, right pyramids, spheres.

Example 1: The cooling system of a car’s 6-cylinder, 250-cubic-inch displacement engine has a capacity of 3.5 US gallons. To protect the engine 
against freezing temperatures, an antifreeze solution of 3/8 ethylene 
glycol and 5/8 water is added to the cooling system. If the cooling 
system is filled to capacity with the antifreeze solution, how many 
quarts of ethylene glycol are in the cooling system?

Example 1: The cooling system of a car’s 6-cylinder, 250-cubic-inch displacement engine has a capacity of 3.5 US gallons. To protect the engine 
against freezing temperatures, an antifreeze solution of 3/8 ethylene 
glycol and 5/8 water is added to the cooling system. If the cooling 
system is filled to capacity with the antifreeze solution, how many 
quarts of ethylene glycol are in the cooling system? Solution: Convert from gallon to quart: 1 gallon = 4 quarts 3.5 gallon 14 quarts 3/8 x 14 = 5.25 The system requires 5.25 quarts of 
ethylene glycol

Example 2: Reshma built 24 wood planters for her garden. The inside of each planter measures 4′ long, 2′ deep, and 1.5 ' wide. She needs to order soil to fill the planters. At K & R Soils, potting soil sells for $17.00/yd3, while Bob’s Best Buy sells potting soil for $21.50/m3. Where should Reshma buy her soil?

Example 2: Reshma built 24 wood planters for her garden. The inside of each planter measures 4′ long, 2′ deep, and 1.5 ' wide. She needs to order soil to fill the planters. At K & R Soils, potting soil sells for $17.00/yd3, while Bob’s Best Buy sells potting soil for $21.50/m3. Where should Reshma buy her soil? Solution: K & R Soils - Covert planter dimensions from feet to yards: 3 ft = 1 yd 4' x 2' x 1.5' feet 1.33 x 0.67 x 0.5 yards V = 0.45 yd3 one planter requires 0.45 yd3 of soil 24 planters x 0.45 = 10.8  Needs 10.8 yd3 of soil 10.8 x $17.00 = $183.60 K & R Soils cost would be $183.60 Bob's Best Buy - Convert planter dimensions from feet to metres: 1 m = 3.2808 ft 4' x 2' x 1.5' feet  1.22 x 0.61 x 0.46 metres v = 0.34 m3 one planter requires 0.34 m3 of soil 24 planters x 0.34 = 8.16 Needs 8.16 m3 of soil 8.16 x $21.50 = $175.44 Bob's Best Buy cost would be $175.44 **** Bob's Best Buy is the best deal.   

Example 3: Mr. Gormley’s Honda Odyssey has a gas tank capacity of 80 L. How much will it cost to fill the tank in Bangor if gas is $3.499 per US Gallon?

Example 4:

Angus has decided to pave his driveway, which measures 74 ft × 18 ft. He has narrowed his choices to concrete or 
paving stones. a) If the driveway is paved with concrete, he will need 4 inches 
 of concrete on top of 8 inches of gravel. b) If he uses paving stones that are 2 1/2 ″ thick, they will 
 need a foundation of 3 1/2 inches of sand and 12 inches 
 of crushed limestone. He will also need to add 10% to his 
 paving stone order to allow for breakage and cutting.

The costs of excavation and materials are shown below. Working in your small group, compare the cost of paving the 
driveway with concrete and with paving stones. Write a report with an itemized cost analysis for both options. Hand In!!!

Time to Work: Page 182 - #3 - 7