1. Hi!
I felt like creating a new topic, so I decided to let you have a look at the following physics problem. I read it in a "newspaper" about technology that we subscribe to.

A 10 cm long (the walls of the cylinder are 10 cm long) cylindrical hole is made in a sphere, so that the hole goes through the entire sphere. How much volume of the sphere is left after making the hole?

(cm^3) a) 300 b)524 c)623 d)714 e)453

P.S. The description is maybe not so accurate, but I hope that you understand what I mean.

2.

3. What's the diameter of the hole?

4. or, at least, the diameter of the sphere

5. The radius of the sphere will not affect the answer (just to point this out).
The radius of the hole depends on the radius of the sphere, if you take into consideration that the walls must always be the 10 cm long.

6. Originally Posted by thyristor
The radius of the sphere will not affect the answer (just to point this out).
The radius of the hole depends on the radius of the sphere, if you take into consideration that the walls must always be the 10 cm long.
hmmm... Are you sure? if so, then the answer is which is approximately answer (b)

7. That is indeed correct. I assume that you used an integral to calculate this (so did I). However, given the five alternatives, there is actually a way to find the correct answer b) without integrating. Can you figure it out?

8. I found the volume of a sphere with diameter 10... so the radius of the cylinder would simply be 0 and as such the remaining volume of the entire sphere.

9. Originally Posted by Arcane_Mathematician
I found the volume of a sphere with diameter 10... so the radius of the cylinder would simply be 0 and as such the remaining volume of the entire sphere.
Yep, this is one of those questions where just knowing that the information given is all the information needed helps with solving the problem.

10. I had to make a spreadsheet to prove it holds for any radius sphere. It does. Interesting.

11. Originally Posted by Bunbury
I had to make a spreadsheet to prove it holds for any radius sphere. It does. Interesting.
In general the volume of what is left after a cylindircal hole of height is bored through the center of a sphere is .

12. Geo, I fail to see the point to your statement.

13. A cylinder doesn't fit into a sphere. It has planar ends.

14. Yes, it does fit. That's a bit like saying you cannot inscribe a square or a rectangle in a circle.

15. Originally Posted by Geo
A cylinder doesn't fit into a sphere. It has planar ends.
No, but a drrill bit goes through a sphere and leaves a hole that is accurately described as right circular cylinder. That remaining body is the volume of the problem.

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