166 replies to this topic

[Brighterthan1000rocks]

Hole in a sphere has been a lot of fun for a long tim. But has anyone yet addressed the question regarding the minimum length of the drill?

Spoiler for answer

radius plus three inches

[Sach]

Spoiler for Bononova, this isn't right.

Spoiler for Here's what is going on .. "the point

The point is that the answer does not depend on the shpere's diameter.
Start with sphere larger than 6" diameter, where it's easy to drill the hole but hard to compute the remaining volume.
Reduce the sphere's size; the hole's diameter shrinks, and the remaining volume gets close to the original volume.
When you get down to exactly 6" diameter, the hole has vanished, and the remaining volume is easy to calculate.
It's precisely the original volume: [4/3]pi*[3in]**3 = 36 pi cu in.

See the bold part. VANISHED implies the hole is not there. Hence, wrong.

[sridharang]

it's just the volume of the cylinder pi*r^2*"6 -4/3*pi*r^3

[aaronbcj]

What if the sphere already had a hole (of the same size of the drill) and you just re-drilled through it? Then the volume of sphere would remain same as before.

[bonanova]

What if the sphere already had a hole (of the same size of the drill) and you just re-drilled through it? Then the volume of sphere would remain same as before.

I guess the answer to that would be a sphere with a hole is not a sphere.

[bonanova]

Spoiler for Bononova, this isn't right.

See the bold part. VANISHED implies the hole is not there. Hence, wrong.

Well, one could say vanishingly small and remove this objection.

For a short, tongue in cheek treatise on the existence of things with attributes of zero, read this.

[Andrew1258]

Spoiler for

I'd like to believe it's 4/3 X 3.14 X 3 X 3 X 3 cubic inches which is the result when the hole's diameter is 0.

[Barron]

Spoiler for well maybe

if you drilled a hole through a round "speaker" there would no longer be any "volume" .....how far out of the box am I??

[bonanova]

Spoiler for well maybe

if you drilled a hole through a round "speaker" there would no longer be any "volume" .....how far out of the box am I??

If the speaker were a sphere, sure ... good one.

[Tbone9]

Spoiler for

I'd like to believe it's 4/3 X 3.14 X 3 X 3 X 3 cubic inches which is the result when the hole's diameter is 0.

Spoiler for I'm with you...

Assuming (or guessing) that the volume remaining will be the same no matter how large or small the sphere is, then we know that as the diameter of the sphere approaches 6", the radius of the hole approaches 0" and the remaining volume is 36pi.