Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 6 Measurement

Problem
Hint
1) How many square feet of synthetic turf are needed to cover the interior of the track shown? The ends of the track are semicircles. Round the answer to the nearest tenth.
1. Since the width of the track is 8 yards and the ends of the track are semicircles, the radius of those ends is ____ yds.
2. Compute the area of 2 of these semicircles = _____ sq. yds.
3. Compute the area of the interior of the track = _____ sq. yds.
4. Add these 2 measurements together and round to the nearest tenth of a sq. yd. = _____ sq. yds.
2) A cereal box measures 14 inches long by 3 inches wide by 20 inches high. The box is completely full. A plastic storage bag is 13.5 inches long by 4 inches wide by 21 inches tall. If you pour the cereal from the box into the bag how full will the bag be? Give your answer as a percent of fullness of the bag, so 100% full means the bag is full. 1. Compute the volume of the cereal box as
    L x W x H = _____ cu. in.
2. Compute the volume of the storage bag the same way = _____ cu. in.
3. Divide the cereal box volume by the storage bag volume and convert to a percent = _____%.

Problem
Hint
3) Joe lives in apartment building that is 70 feet long by 60 feet wide by 80 feet tall. The volume of the building next door is 252,000 cubic feet with the same length and width as Joe's building. What is the difference in height in feet between the two buildings? 1. Multiply the length by the width = _____ sq. ft.
2. Divide the volume of the building next door by this area =
    height = ______ ft.
3. Compute the difference between these heights = _____ ft.

4) A loop of rope has a total length of 30 feet. If you create a rectangle with the loop that has length 8 feet, and then create a second rectangle with length 10 feet what's the difference in the area of the two rectangles?
1. Compute the width of the first loop as the
    (total length - 2 x the length of the rectangle) / 2 = _____ ft.
2. Compute the width of the second loop as the
    (total length - 2 x the length of the second rectangle) / 2 = _____ ft.
3. Compute the areas of the 2 rectangles and subtract = _____ sq. ft.

5) 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 tablespoons = 1 cup, 1 cup = 8 ounces, and 1 gallon = 128 ounces, how long will it take before the bucket is full? Express your answer in hours, minutes and seconds.
1. If 3 drops = 1 teaspoon, then ____ drops make a tablespoon.
2. Convert this to cups = _____ drips/cup.
3. Convert this to ounces by diving by 8 = ____ drips/ounce
4. Multiply by the number of ounces in a gallon to get the number of drips/gallon = _____.
5. Multiply this by 3 to get the total number of seconds to fill the bucket = _____ seconds.
6. Convert this to hours, minutes, seconds =
    ____ hours ____ min ____ sec.