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Washington State Math Olympiad
Hints and Solutions
2006 Grade 7 Geometry
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1) A cube sculpture is created from cubes stacked on top of each other and next to each other. Cubes that are stacked meet along their square faces. The top view, front view, and side view of a cube sculpture are given below, where only the squares directly facing you from each view point are shown. What is the least number of cubes you would need to add to the sculpture to make it a solid rectangular prism of cubes?
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2) The parallel lines are 1 unit apart. What is the area of the shaded pentagon?
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3) Jill decided to rearrange her room. She will rotate the
bed and table counter clockwise 90 degrees about the center of
her room. The center of the room is given by the origin.
The original coordinates of the table were (0, -4), (2, -4),
(2, -6), (0, -6). What will be the new coordinates of the
table?
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5) Mr. Bill is going to make a pouf (a foot rest) out of a rectangular piece of leather that measures 6 feet by 3 feet. His pouf will be a cylinder and he will stuff it with newspapers.
The top and bottom will be circles, and the side will be made from one long rectangle that wraps around the top and bottom circle, see the shaded region. He will use the layout
below that has the height of the pouf smaller than the diameter. How tall will he make his pouf in feet? Give your answer in exact form in terms of 
or as a decimal to the nearest
tenth of a foot.