Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 8 Measurement
Problem
Hint
1) Mikki's Ice Cream is planning on changing their ice cream packaging from rectangular cartons to cylindrical containers. Their cartons measure 7 in x 5 in x 4.5 in. To keep the amount of packaging about the same they would like the surface area of the carton to be the same as the surface area of the new cylindrical containers (top + bottom + side). The height to diameter ratio should be 1.5 to 1. What are the radius and height of the cylinder to the nearest tenth of an inch?
Use = 3.14 or provide an exact answer.
  1. The surface area of the rectangular cartons is


    _____ sq. in.
  2. Using h for the height of the cylinder and d for the diameter, the surface area of the cylinder (don't forget the ends!) =



    _______________
  3. Simplify, set equal to the rectangular box surface area and somve for the radius and the height:



    r = ____

    h = _____
2) A turtle is racing a hare. The race course is 60 feet long. The turtle trundles along at a rate of 40 ft per hour without resting. The hare hops along at a rate of 60 ft per hour but rests for 15 minutes every 25 feet.
a. How does the race end?
b. What is the distance between the winner and loser?
  1. The turtle takes _____ hours
  2. Compute the times the hare takes for his alternate hops, rest, hops, rests and compute how long it takes him to get to the 60 feet. Compare that to the turtle's time.

Problem
Hint
3) A goose is being tracked on its migration south by a tiny device. Its flight path for two legs of its journey is shown on the grid which is centered at Walla Walla, numbers are in miles. How far did the goose fly over the two legs of the journey? Express your answer to the nearest mile. Use the pythagorean theorem to determine the flight path lengths.
4) The diameter of Earth is 1.28 x 104 km and the diameter of Jupiter is 1.43 x 105 km. Assume both planets are spheres. How many times larger to the nearest whole number is Jupiter's surface area than Earth's surface area? Surface area of a sphere: 4 r2 , where r is the radius. Compute the Earth and Jupiter's surface areas and divide Jupiter's by the Earths.




ratio = ________

5) Dorey goes to Italy and Greece every year for about half the year. She brings back clothing to sell. At the beginning of her trip the dollar euro exchange rate is $1.00 = € 0.66. She buys 10 silk blouses at € 35.00 a piece. When she returns to the US the exchange rate is $1.00 = € 0.78. Does the cost in dollars for one silk blouse go up or down from the beginning to the end of her trip and by how much?.
  1. Cost of blouses in dollars = ______/blouse

  2. Converting back to dollars at the end of the trip = _______

  3. The cost in dollars went ______ by _________