Snowman Geometry – The Problems
December 15, 2008
For the following problems assume that the snowballs are perfect spheres.
Chiquita and Rhonda are each building a snowman. Rhonda tells Chiquita that she is making each of her 3 balls of snow 20% smaller than the one below it. Rhonda starts by making the base ball with a diameter of 20 inches. If she reduces the diameter by 20% each time she makes a new ball, what is the diameter of the third ball she makes (the ball for the snowman’s head)? Express your answer as a decimal to the nearest tenth.
Chiquita planned to do the same thing as Rhonda but she misunderstood what Rhonda meant when she said “…20% smaller than the one below it.” Chiquita made her first ball the same size as Rhonda but then decreased the volume by 20% for each subsequent ball. How much taller is Chiquita’s completed snowman than Rhonda’s completed snowman? Express your answer as a decimal to the nearest tenth.
Rhonda’s little brother, Benjamin, comes outside and decides to make a snowman out of cubes of snow instead of balls. If each of his three cubes has a side length equal to the diameter of the corresponding ball on Rhonda’s snowman, how many more cubic inches of snow did Benjamin use than Rhonda? Express your answer as a decimal to the nearest tenth.
The solutions to this week's problems will be posted in the archive on Monday, December 22nd, 2008.