Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 7 Measurement
Problem
Solution
1) A garden has the shape shown with center a square and two semicircles joining on opposite sides of the square. How many square feet is the garden? Round the answer to the nearest square foot.
  1. The 2 half-curcles make a full circle together whose area is
    12.52 = 156.25 sq. ft.
  2. The area of the square is 625 sq. ft.
  3. Together, the total area is :
    156.25 + 625 = 490.625 + 625 = 1115.625 sq. ft. = 1116 sq. ft.
2) Find the area of the S shaped figure.
Give an exact answer.
(express your answer in terms of )
  1. The figure consists of 2 3⁄4 circles = 3⁄2 circle
  2. So the area of the total figure is:
    3⁄2 x 222 =
    726 sq. mm.
3) The rim of a car wheel has radius 8.25 inches. The car tire measures 3.5 inches from where it meets the rim to where it meets the road. How much larger is the outer circumference of the tire than the circumference of the rim to the nearest tenth of an inch?
  1. Circumference of the rim = 16.5 in.
  2. Circumference of the tire + rim = 23.5 in.
  3. Difference =
    23.5 - 16.5 = 7 = 21.98 = 22 inches

Problem
Solution
4) Margie sees that she has a steadily dripping faucet in the tub that she can not turn off. She places a 1 gallon bucket underneath it. The faucet drips at a rate of one drop per 3 seconds. 3 drops make a teaspoon. If 3 teaspoons = 1 tablespoon, 16 tablespoon = 1 cup, 1 cup = 8 ounces, 1 gallon = 128 ounces, how long before the bucket is full? Express your answer in whole numbers of hours, minutes and seconds. Work this problem backwards.
  1. 1 gallon = 128 oz = 16 cups = 256 tablespoons = 768 teaspoons = 2304 drops
  2. 2304 drops x 3 seconds/drop =
    6912 seconds to fill the bucket.
  3. 6912 seconds = 1 hour 55 minutes 12 seconds

5) Pictured below is the drawing of a wood block from a toy set that looks like two steps. The drawing is not to scale. The height of the two steps and the width of the bottom step are all the same given by D. The total height of the steps marked with A is 2 cm. The width of the bottom of the block labeled with B is 2.5 cm. The length of the block given by C is 3 cm. Find the surface area of the entire block.
  1. Since 2 Ds make A, D = 1 cm.
  2. Back: 3x2 = 6 sq. cm.
  3. Sides 2(2.5x2 -1x1) = 8 sq. cm.
  4. Top: 1.5x3 = 4.5 sq. cm.
  5. Bottom: 3x2.5 = 7.5 sq. cm.
  6. 3 parts of the steps = 3(3x1) = 9 sq. cm.
  7. Total = 6 + 8 + 7.5 + 9 = 35 sq. cm.