Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 8 Geometry
Problem
Hint
1) The circumference of a major league baseball is 235 mm. If the volume of a sphere is given by the formula V = 4/3(pi)r3, where r is the radius, what is the volume of the baseball to the nearest cubic mm? (Use 3.14 for pi)
  1. First, find the radius of the baseball:


    ___________
  2. Then compute the volume =


    __________________

2) Write the letters M, T, and H in the correct orientation on figure 1 so that when the net is folded into a box, it will spell MATH vertically as shown in Figure 2.
Visualize these moves in your mind:
  1. Fold the 2 spaces to the left of the "A" in.
  2. Fold the 2 spaces to the right of the "A" in.
  3. Now fold the 2 upper spaces on the right down.
  4. You should be able to figure out where the letters go and what orientation they should be in.
  5. Write them in on the figure to the left.
3) Farmer Cobb is trying to construct a pen with 8 sections of fence that are each 18 feet long. The sections are rigid and cannot be bent. What is the greatest area he could encompass with the pen? (Round your answer to the nearest tenth of a square foot)
  1. Consider that if you had 1000 sections how would you make the largest area with them? You would approximate a circle with them!
  2. The figure that 8 sections can make that most closely approximates a circle is an __________
  3. This page about areas of regular polygons should be helpful.

    Area = _________________

Problem
Hint
4) On an analog clock, you observe that the angle between the hour and the minute hands is 90 degrees at 3 pm. What will the angle between the hands be 35 minutes later? Express the answer to the nearest tenth of a degree. (Both hands move at different constant rates)
  1. The entire clock face has 12 hours.
  2. You must figure out how much the hour hand moves and how much the minute hand moves.
  3. For each hour, the hour hand moves _____ degrees.


    Angle = _____________
5) What is the area of the shaded region of the square, with an equilateral triangle inside, with a side length of 5 units? (Express your answer to the nearest hundredths of a square unit)
 Method 1: Compute the area of the triangle and subtract:
  1. Using the pythagorean theorem, the height of the equilateral triangle (h) is



      __________




  2. Area of the shaded region = _________
Method 2: Use the formula for the area of an equilateral triangle
  1. The formula for the area of an equilateral triangle is:
    s2(√ 3  ) / 4
  2. Work this out using the problem parameters





    The shaded area is _______ units.