TJ Prep Problems

TJ test prep practice problems  for our students and readers. The problems provide a very small sampling of what Optimal TJ Prep students work with.

A Geommetry Problem for TJ/AOS/Blair/SHSAT Test Prep (Medium). Target Time. 20-45 seconds.

Two concentric (with the same center) spheres such that the radius of the smaller sphere is 1/3rd the radius of the larger sphere. What is the ratio of the volume of the space between the two spheres to the volume of the smaller sphere? Note. Volume of a sphere = 4/3rd Pi r^3 where Pi is approximately 22/7. Hint. The best way to solve the problem is not to use the formula for volume of a sphere.