Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 7 Geometry
Problem
1) Write the letters M, T, and H on Figure 2 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.

2) The figure shows a drawing of a pyramid tower climbing toy located in a park. It is constructed with large congruent wooden cubes solidly nailed together. The volume of one wooden cube is 1000 cu. inch. What is the visible surface area in square inches? This includes the exposed north, south, east and west faces and looking top down.?

Problem
3) In the diagram of nested squares each next square is inscribed in the previous square with its vertices bisecting the sides of the previous square. What fraction of the area of the largest outside square is shaded?
4) A dog food company wants a bigger can size and a new look. It considers doubling the diameter or doubling the height. What is the ratio of the volume of the doubled diameter can to the volume of the doubled height can?
(Volume of a cylinder is r2 h )

5) The triangle with vertices (0,0), (3,0) and (0,4) is rotated by 90 degrees counterclockwise around the origin, the image is rotated by another 90 degrees counterclockwise around the origin, and that image is rotated by another 90 degrees counterclockwise around the origin to produce four triangles. Create a single figure by shading all four triangles. How many points that have integer values for both the x and y coordinate are in the interior of the shaded figure?