Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 8 Measurement
Problem
1) Find the area of the S shaped figure. Give an exact answer, so express your answer in terms of
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?

Problem
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?
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?
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?