Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 8 Geometry

Problem
1) A garden is laid out as a set of four half circles, see diagram. The ratio of the diameters of the three smaller circles is 2 to 1 to 3. What is the ratio of the distance for walking from A to B along the outer edge of the single large circle compared to the distance for walking from A to B along the outer edges of the three smaller circles?
2) The folding pattern below folds to a pyramid with base a square with side length 2 units and isosceles triangles for sides with height 3. What is the height of the resulting pyramid?
Express your answer to the nearest hundredths.

Problem
3) In the big 3 x 3 square, what is the ratio of the shaded four triangles to the unshaded octagon in the middle of the square? The octagon is not regular but is a truncated square. All line segments are intended to be straight.
4) The line given by the equation y = 3x - 3 is translated 3 units up and then reflected across the line y = 0. What is the equation of the new line?

5) A circular cone can be created by joining the two straight edges of the shown section of a circle with central angle 135 degrees and radius 5 centimeter. What is the diameter of the created cone? (The diameter of a cone is the diameter of the circular opening where it is the widest.)