Activities

1. A company is making cubes that measure inches.  How much material will they need to make each cube?

2. Find the volume of space inside the tent for the family to sleep.

3. Paul is installing a fence around his pool, which is made up of a rectangle and a semicircle, as shown in the diagram below.  Determine the amount of fencing, to the nearest tenth of a foot that Paul will need to go completely around the pool.

4. Kara wants to tile the floor shown in the accompanying diagram.
   If each tile measures 1 foot by 1 foot and costs $1.98, what will be the total cost, including an 7% sales tax, for tiling the floor? Round your answer to the nearest cent.

5. A lawn service is trying to figure out how long it will take them to mow a new client’s yard.  The new yard is acres.  Currently the mow a lawn that is 50 yards by 26 yards in 1 hour.  One acre of land is about 4850 square yards.  How long will it take the lawn service to mow the new yard? Round your answer to the nearest tenth, and then change it into minutes and hours.  Show your work.

6. Jacob buys his ice cream in a rectangular prism-shaped carton, while Cindy buys hers in a cylindrical-shaped carton. The dimensions of the prism are 6 inches by 4.5 inches by 5 inches. The cylinder has a diameter of 5 inches and a height of 7 inches. Which container holds more ice cream?  How much more ice cream the larger container holds? Show your work and round your answers to the nearest tenth.

Answer Key/Rubric

1. V = inches³ of material

2. V= 288 feet³

3. The total amount of fencing needed is 80.8 feet.  Student work might include but is not limited to,

• Around the rectangular part of the pool is 25+25+12 = 62 feet
• Around semi-circle  C = ∏ D
• C = 3.14 * 12
• C = 37.68
• It is a semicircle so it needs to be cut in half
• 37.68 ÷ 2
• 18.84 ≈ 18.8
• 62 + 18.8
• 80.8 feet

4. The total cost would be $127.12, Student work might include but is not limited to,

• The shape must be broken up into 2 separate rectangles to find the area.
• A = bh
• A = 9 x 5
• A = 45 ft2
• Find the side length of the second rectangle that is not given
• 10 – 5 = 5
• A = bh
• A = 3 x 5
• A = 15 ft²
• Add the two areas to find to total area
• 45 + 15 = 60 ft²
• This means to you need 60 tiles that each cost $1.98
• 60 x 1.98 = 118.80
• Tax is 7%
• 118.80 x 1.07 = 127.116
• Total cost is $127.12

5. The total time that is will take the lawn service to cut the lawn is 5 hours and 36 minutes.  Student work might include, but is not limited to,

• The service can mow 50 x 26 = 1300 yards in one hour
• 
• The new lawn is a total of 1.5 x 4850 = 7275 yards
• Find the amount of time it will take to cut the new yard
• The new service will take 7275 ÷ 1300= 5.596
• Round the answer to the nearest tenth and convert the time to hours and minutes.

• That rounds to 5.6 or
• The total time is 5 hours and 36 minutes.

6. The cylinder holds more than the rectangular prism.  It holds 2.4 inches³ more.  Student work might include but is not limited to,

• Find the volume of each container
• Find the volume of the rectangular prism
• V = lwh
• V = 6 x 4.5 x 5
• V = 135 inches³
• Find the area of the cylinder
• V= Bh
• V = ∏r² x h
• Find the radius by dividing the diameter in half 5 ÷ 2 = 2.5
• V = 3.14 x 2.5² x 7
• V = 137.375
• V ≈ 137.4 inches³
• The cylinder holds more than the rectangular prism.
• The difference in the volumes is 137.4 – 135 = 2.4 inches³