Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2017 Grade 7 Geometry
Problem
Hint

1) How many cubes with a 3 inch side would fit in a box with dimensions 12 inches by 15 inches by 9 inches?
  1. Compute the volume of the box = ______________ cu. in.
  2. Compute the volume of the cube = _________ cu. in.
  3. Divide the volume of the box by the volume of the cube to get the number of cubes that will fit in the box = _______ cubes.

2) What is the measure of angle x? (not drawn to scale).
 Please note: The arrows on the 2 horizontal lines indicates that they are parallel. A little tricky!
The applicable missing angles have been labeled a,b,c and d on the diagram.
  1. Angle a is _______ degrees
  2. The arrow lines are parallel, therefore angle d = angle ____ = _____ degrees
  3. Angle c is vertical with the 71 degree angle and is therefore ______ degrees
  4. Angles x, d, and c sum to 180 degrees, so x = _____ degrees.

3) ABCD is a square with side length 20 inches. A, B, C, and D are all the centers of 4 congruent circles that touch each other as shown in the picture. Find the area of the shaded region. Round your answer to the nearest whole number.
  1. The area of the square is _____ sq. in.
  2. The 4 quarter circles sum to a full circle of radius _____ in, so the circle area is _____ sq. in.
  3. The shaded region area is the difference between these 2 areas = ______ sq. in.

Problem
Hint

4) In triangle ABC, Angle A's measure is twice angle B's measure. Angle C's measure is 41⁄2 times A's measure. What is the measure of angle A?
  1. The total measure of all angles of the triangle in terms of A are _____
  2. Since these angles add to 180, then A = _____ degrees.

5) Which shape has the greatest volume? (not drawn to scale)
  1. Volume of a triangular prism = ________ cu. m.

  2. Volume of the rectangular prism = _______ cu. m.

  3. Volume of the cylinder = ______ cu. m.

  4. Therefore the ____________ has the greatest volume.