Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 7 Measurement
Problem
Solution
1) Ms. Creeley's class is doing a canned food drive. All the cans will be placed in a large cylindrical barrel that Ally and Joe are going to decorate like a can of stew. The barrel has a radius of 18 inches and is 3 feet high. They plan to first cover it in sheets of 9 inch by 14 inch construction paper. The art teacher will give them the construction paper only if they tell her what is the fewest number sheets they will need. How many sheets will they need if they cover only the sides of the barrel? Remember, they can only get whole sheets.
  1. The surface area of the barrel is
    36 x 36 in = 1296 sq. in.
  2. The area of one sheet of construction paper is 9x14 = 126 sq. in.
  3. The number of sheets needed = 1296x3.14/126 = 33 sheets

2) Dariel made his own home trash compacting device. It is in the shape of a rectangular prism with dimensions 2 feet by 18 inches by 4 feet tall. At the top is a level plate that is pushed straight down on the trash. It is lowered at a rate of 1 foot per 15 seconds. If the trash compactor bin is full to start with, by how many cubic feet is the volume of trash reduced after 30 seconds?
  1. After 30 seconds the compactor has traveled 2 feet.
  2. The area of the top of the compactor is 24x36 = 432 sq. in
  3. The volume of the reduction is 432x24 = 10368 cu. in.
  4. 10368 / 1728 = 6 cu. ft.
3) An inflatable pool is being filled using two hoses. One hose can fill a 1 gallon bucket in 30 seconds, the other can fill the same bucket in 20 seconds. If the hoses are left on for 20 minutes how many gallons of water are there in the pool?
  1. Hose #1 rate = 2 gallons/minute
  2. Hose #2 rate = 3 gallons/minute
  3. Combined rate = 5 gallons/minute
  4. 5 gallons x 20 minutes = 100 gallons
       minute

Problem
Solution
4) A wooden shipping crate is measured for shipping. Its length is 8 feet and its girth (going completely once around in the direction perpendicular to the length) is 24 feet. The surface area of the lid of the crate is 40 square feet. The dimensions are whole numbers of feet. What is the volume of the crate in cubic feet?
  1. If the top area is 40 sq. ft. then the width of the lid is 40/8 = 5 ft.
  2. Using the girth of 24 feet, the other dimension must be (24 - 10)/2 = 7 feet.
  3. Therefore the volume is 8 x 5 x 7 =
    280 cu. ft.
    See the figure to the left for these dimensions.
5) On Tuesday, March 6 Shelby looks at her digital clock and it reads 6:40 and 00 seconds. Exactly a week later down to the second by her atomic watch (which keeps perfect time), Shelby looks at her digital clock and it reads 6:50 and 00 seconds. What time will it show to the nearest second in exactly 48 hours if she leaves the clock alone?
  1. The digital clock gains 10 minutes over 7 days
  2. 48 hours is 2 days, so the clock will gain
    10 minutes x 2 days = 2 minutes 51.42 seconds
        7 days
  3. It will show 6:50 + 2 minutes 51 seconds =
    6:52 and 51 seconds