Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 8 Geometry

Problem
1) In the diagram there are two parallel line segments and a labeled line segments R that meets the line segments at a 30 degree angle. On your answer sheet, sketch what the result is when you reflect the two parallel line segments across R. What are the measures of the new angles formed between the reflected line segments and line segment R?

2) A circle is enlarged by increasing its radius by 50%. What is the ratio of the area of the enlarged circle to the area of the original circle?

Problem
3) The isosceles trapezoid ABCD is the union of two smaller trapezoids ABFE and EFCD. AB has length 8 units, EF has length 4 units and DC has length 2 units. The area of trapezoid ABCD is 20 square units. What is the height of trapezoid EFCD?
4) An isosceles triangle has vertices at (-5, 1), (5, 1), and (0, 8). How many points lying in its interior also have only integer coordinates?

5) The circumference of the bowling ball is 27 inches. If the volume of a sphere is given by V = 4/3 r3, where r is the radius, then what is the volume of the bowling ball to the nearest tenth of a cubic inch?
Use = 3.14 in your computations or give an exact answer leaving in your answer.