Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 8 Measurement
Problem
Solution
1) You are racing in a soap box derby. The front wheels of your car are 6 inches in diameter and the rear wheels are 10 inches in diameter. How many more rotations will a front wheel make compared to a rear wheel over the course of a 989-foot track? (Round your answer to the nearest full rotation))
  1. Circumference of the 6-inch diameter wheel = 6 inches
  2. Circumference of the 10-inch diameter wheel = 10 inches
  3. Number of rotations of the small wheel in a 989-foot track =
    989x12/6 = 629.6 revolutions
  4. Number of rotations of the large wheel in a 989-foot track =
    989x12/10 = 377.8 revolutions
  5. Difference = 629.6 - 377.8 = 252 rotations
2) The square plate of metal seen below is punched with holes along each edge. The center of each hole is spaced 2.3 cm apart from each other hole and spaced 4.2 cm away from the edge of the plate. What is the surface area of the metal plate before the holes were drilled? Express your answer to the nearest hundredth square centimeter.
There are 3 center-to-center spaces and 2 edge spaces in each dimension.
  1. Width = 4.2x2 + 2.3x3 = 15.3 cm
  2. Area = 15.32 = 234.09 sq. cm.

Problem
Solution
3) Olga is building a cork board for her father. Her original dimensions for the board are 80 cm by 130 cm, but she decides to make each side 20% longer for the final construction. By what percent will the area of the board increase? An increase of 20% is to multiply the dimension by 1.2.
To determine the percent increase you really don't need the actual dimensions!
    (1.2)2 = 1.44 = 44% increase
4) A cylindrical grain silo measuring 20 feet tall with a diameter of 10 feet is being emptied. It takes 48 seconds to empty a cubic foot of grain. How long will it take to empty the silo if it started out full? Express your answer to the nearest minute.
  1. Volume of the silo = 20 x 52 cu. ft.
  2. Time to empty = 48 x 20 x 25 =
    75360 seconds = 1256 minutes
    (using 3.14 for )

5) If you take a cube and shrink each length by a factor of 3, what is the ratio of the final surface area to the initial surface area?. 		    (1⁄3)2 = 1⁄9