Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 8 Measurement

Problem
Hint
1) Find the area of the S shaped figure. Give an exact answer, so express your answer in terms of
  1. The figure consists of _____________ full circles.

  2. So the area of the total figure is:


    _____ sq. mm.
2) An ice cream cone is a right circular cone. The volume of a right circular cone is 1/3 the volume of the cylinder that has the same radius and height. A small cone has radius 1 inch and height 4 inches. A large cone has double the radius and double the height, so 2 inch radius and 8 inch height. What is a good estimate for the scale factor giving the change in volume of ice cream the large cone can hold compared to the small cone?
  1. Small cone volume: _______

  2. Large cone volume: _______

  3. Scale factor = ______
3) The triangle has a base of 5 and a height of 12. A rectangle is formed with the same base as the triangle and with the height the length of the hypotenuse of the triangle. What is the area of the rectangle? Call the hypotenuse h.
  1. By the pythagorean theorem:

    h =


    _____ cm.

  2. Area of the rectangle = ______ sq. cm.

Problem
Hint
4) A teacher hands her student a block of wood with dimensions 2 inches x 3 inches x 5 inches and asks "What's the longest toothpick you could make out of this block?" What is the correct response to the nearest whole number of inches?

Apply the the pythagorean theorem first to the 3x5 side to find its diagonal and then to the 2 inch side with this diagonal to find the length from opposite corners of the block of wood.




Max length of a toothpick = _____ inches.
5) Maria is creating a folding pattern for a dodecahedron on the computer. She has attached two pentagons together along one edge. What is the measure of the outside angle created at point A by the two pentagons as shown in the diagram? The formula for the measure of the interior angles of a polygon is 180(n - 2) / n, where n is the number of sides.
  1. For our pentagon the interior angles are

    _____ degrees.
  2. Therefore the outside angle A is

    _____ degrees
Note: This formula for the measure of the interior angles of a polygon is one you should memorize