A young doctoral candidate was taking his orals. He had with him his super-high-tech calculator and several reference books containing all the formulas he needed. One crusty old professor posed the following math problem.
"You have a ball with a cylinderical hole through the middle. The height of the cylinder (hole) is 6 inches. When submerged in a bucket of water, it displaces about 113.09724 cubic inches." (Which the PhD candidate immediately recognizes as 36π in^3.)
Now sez the professor, "What is the diameter of the ball before we put the hole in it?"
The candidate's degree depends on his answer. What should it be?
2007-06-08 08:02:13 · 5 answers · asked by davec996 4 in Science & Mathematics ➔ Mathematics
The height of the hole is 6", That is the height of the cylinder. The radius of the ball is bigger.
2007-06-08 08:22:02 · update #1
Correction: The diameter of the ball is bigger!
2007-06-08 08:24:13 · update #2
Answer: The PhD candidate should say that the radius of the ball is indeterminate. Could be any number > 6"
This is one of those oddities that you happen across now and again. The volume of the ball is the initial volume (1.333πr^3) minus the volume of the cylinder and minus the volume of the two "caps" at the end of the cylinder. The volume is always 36π regardless of the radius.
Things I learned on the way to looking up other things.
2007-06-10 05:18:26 · update #3
This is a famous problem, and it turns out that the diameter of the hole doesn't matter (although it is related to the diameter of the ball). Assume that the hole diameter is arbitrarily small. Then the radius of the ball is the cube root of 27, which is of course 3. So the diameter is 6. In the usual statement of this problem, the length of the hole is given (or to be determined) from the volume.
2007-06-08 08:09:38 · answer #1 · answered by Anonymous · 0⤊ 0⤋
6 inches
2007-06-08 08:08:39 · answer #2 · answered by gecham 2 · 0⤊ 0⤋
You will need to set up the integral to calculate the volume of the solid, and look at it real hard. There is a surprise.
2007-06-08 08:18:32 · answer #3 · answered by donaldgirod 2 · 0⤊ 0⤋
The cheap answer would be "the same as it is after you put the hole in it".
Otherwise...I would guess 6 in.
2007-06-08 08:13:36 · answer #4 · answered by Mathsorcerer 7 · 0⤊ 0⤋
are you trying to cheat?
2007-06-08 08:11:26 · answer #5 · answered by Anonymous · 0⤊ 0⤋