Question

I can't understand the problem:

Let 0 < a < b. Consider a ball of radius b and a cylinder of radius a whose axis passes through the center of the ball. Find the volume of the ball with the cylinder removed.

Answer 1

How can we tackle this is we know nothing about the height of the cylinder?

Answer 2

You will have an answer in terms of some dimension, either cylinder or sphere.

Answer 3

I don't see any relation between the two in the text of the problem.

As far as I am concerned the answer is 4/3pi^3 because H is an infinitesimal.

Answer 4

Draw a sketch.
If you do you will see that many different cylinders could be drawn. OK?

Answer 5

Infinite number of cylinders

Answer 6

Nah.

Answer 7

I think it is no more complicated than vol(sphere) - vol(cylinder).

Answer 8

My first answer was misleading.

Answer 9

Its supposed to be a problem on solid's volume through disks or Washers

Answer 10

But I fail to see any constraints on cylinders height in it

Answer 11

Why not 4/3 pi b^3 = pi a^2 h
And the problem, I see it now, is what is the height of the cylinder given a and b.

Answer 12

It's Pythagoras again!

Answer 13

Are you with me?

Answer 14

no, why are you equating two different volumes?

Answer 15

Sketch the problem, it will be clear.

Answer 16

Shall I

Answer 17

sphere radius is b
diameter radius is a
problem is to find the volume of sphere - cylinder
OK?

Answer 18

sorry cylinder radius is a

Answer 19

Why it cant be like this?

Answer 20

Yes. You are right. But I bet that's not what they mean.

Answer 21

I hate poor definitions in math textbooks (

Thanks for help.

Answer 22

So, given the cylinder radius, you can get the height, given the radius of the circle. If the cylinder doesn't touch the top, you can get anything.

Answer 23

pretty much

Answer 24

was fun

Answer 25

And you had the right question at the beginning! lol as they say