Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 6 Geometry
Problem
1) Lamar wants a circular pool in his back yard. He maps out the circle and decides it is far too small. If Lamar increases the diameter by 6 feet, it doubles the circumference. What is the circumference of the bigger circle?
You may leave your answer in terms of
or use = 3.14 and round to the nearest tenth.

2) Some of the vertices of a polygon are located at the coordinates
(-2, 1), (2, 2), and (4, 4). The polygon has a vertical line of symmetry at x = 4 which meets the opposite edge at the midpoint (4, 1). Name the polygon that has the fewest number of vertices satisfying these conditions, and give the coordinates for one its other vertices.

Problem
3) In the pyramid of cubes shown, what is the minimum number of cubes that would need to be added to complete it to a solid cube?
4) Write the letters M, T, and H on figure 2 on the answer sheet so that when the figure is folded into a box, it will spell MATH around the sides of the box. Figure 1 shows the correct placement of the letters.
5) An animator creates the idea of a rolling eye by having a circle roll around the inside of a larger circle. If the radius of the larger circle is 2 cm and the radius of the small circle is 3/4 cm, what is the area of the large circle that is never touched by the small circle?
You may leave your answer in terms of
or use = 3.14.