Question

Four spheres and three cubes are arranged in a line according to increasing volume, with no two solids of the same type adjacent to each other. the ratio of the volume of one solid to that of the next largest is constant. if the radius of the smallest sphere is ¼ that of the largest sphere, what is the radius of the smallest sphere?

Answer 1

You have four ping pong ball sized spheres, all with a diameter of 4 cm. You have three on the fl oor, all touching one another, so that they form a little triangle. The fourth ball is placed on top of that triangle of balls, so that it’s touching all three of the other balls (Fig. 1 & 2). The Question: How tall is that stack of balls, from the bottom of the three balls, to the top of the fourth, middle ball (Fig. 3)? How We Can Look At The Problem: To start, we need to fi nd the center of the bottom balls. It is important to note that the top ball is not sitting in the center of the box, since the centroid of the triangle of the bottom balls does not overlap with that of the box.