Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 8 Measurement
Problem
Hint
1) A full can of paint contains 45 cubic inches of paint. It takes 1/3 of the can to paint one side of a door that is 6 feet 8 inches tall and 3 feet 4 inches wide. How thick is the paint on the door? Express your answer as a fraction of an inch reduced to lowest terms.
  1. Compute the volume of 1⁄3 can of paint = _____ cu. in.

  2. Compute the area of the door in sq. in.

    = _________________ sq. in
  3. Use this area and the volume to compute the thickness:


    Thickness = _________ in.

2) The Telinos are tiling their bathroom. Part of the design will be a zigzag band all around the room. To create this they will need to cut white triangles and grey parallelograms from rectangle tiles. The rectangles have dimensions 4 cm by 12 cm as labeled. The triangles have height 7 cm. What is the perimeter of a parallelogram tile in centimeters? Round to the nearest centimeter.
  2. Compute the missing length of the diagonal which is the hypotenuse of the triangle using the pythagorean theorem:



    C = ____ cm.
  3. Add up the sides:



    Perimeter = ____ cm.

Problem
Hint
3) Shauna enters a bike race. She checks out the course one weekend and it takes her two hours to ride the course. If she rides at an average rate of 18 mph for the first third of the time, speeds up to 25 mph for the next 1/4 of the time, slows to 12 mph for the next 1/4 of the time and finishes with a speed of 27 mph for the last 20 minutes of the course, what is her average rate in miles per hour? Express your answer to the nearest tenth of a mile per hour.

 Compute the distances for each leg and add:
  1. Leg 1:

    _____ miles
  2. Leg 2:

    _____ miles
  3. Leg 3:

    _____ miles
  4. Leg 4:

    _____ miles
  5. The course is _____ miles long.

  6. Average rate = _____ mph.
4) Brad and his parents get to tour a house that is a right circular cone. It is three stories high and a circular staircase goes up the center. Brad would like to have the top floor as his bedroom. The brochure says the first floor has a diameter of 50 feet. The inside height of the house measured up the center of the staircase to the very top is 38 feet. The circular staircase uses a circular area with diameter 6 feet on all three floors. The room heights are all 12 feet with 1 foot thick floors separating the stories. What is the area, to the nearest whole number, of the floor of Brad's dream bedroom not including the circular staircase area?
  1. Use the ratio of the width of the cone to it's height to determine the width of the top floor:


    = _____ feet.
  2. It's area is _____ sq. ft.
  3. Subtracting the staircase:



    = _______ sq. ft.

5) James loves chocolate milk and has an idea. He plans to invent chocolate milk cubes that you can add to milk, shake and create instant chocolate milk. He knows that bouillon cubes have side length 1/4 inch and weigh 4 grams. He thinks his cubes should have side length 1/2 inch. Assuming bouillon cubes and his chocolate milk mix weigh the same by volume, how much will one of his chocolate milk cubes weigh to the nearest gram? 		Each dimension is 2 times the bouillon cube dimension so his cube is ____ times the volume.

The larger cube's weight is _____ grams.