Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 8 Geometry
Problem
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)

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.

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)

Problem
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)
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)