Question

A ball of radius 11 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid.

Answer 1

Find the volume of the ball and then subtract the volume of the hole.

Answer 2

that is what i have been trying. a ball is a sphere so v= 4/3r^3 and the hole is a cylinder pi*r^2*h but what is h the height it isnt the diameter of the sphere

Answer 3

The height is the the radius of the ball times 2 (Diameter) :)

Answer 4

a cylindrical hole would be slightly shorter than the diameter of the sphere the thing is idk how to find that

Answer 5

If you are going to picture this out in your mind, or better yet, get a pen and paper and draw it.. You will find out that it is the height of sphere. Operative word is "center of the ball".

Answer 6

i did do that and i believe it was the diameter, but after some rethinking, as well as the answer being wrong i saw a different picture. Imagine a sphere. it is round obviously if you drill a hole threw it the the whole will be a cylinder. Cylinders have flat bases. A flat base would mean it cuts off before the end of the sphere. if the height was the diameter it would mean that the base is curved

Answer 7

afs brings a good point
did you learn triple/double integrals yet?
i believe that that is the only way to get the answer

Answer 8

Oh yeah! Figured that one out thanks for the clear description. @_@

Answer 9

We are at area between curves and volume between curves. i kind of know how to do those, but this, which is one of them, doesn't give all the info, all i need is the height and im good but dont know the height. :(
@ mcometa :D

Answer 10

i think you can do this using what you do
do you know the washer method yet?

Answer 11

i zoned out for that one, im using the shell method, but i dont know how exactly to apply it to this

Answer 12

ehh...i'm not sure what the shell method is
LOL
but the washer method is bascially integral curve1-curve2

Answer 13

Are you doing this in polar? or spherical?

Answer 14

And is this calc 3 or calc 2

Answer 15

so now imagine your cylinder and sphere on the xy plane
ONLY the xy plane
you'll see a circle and a rectangle
curve1 will be the circle and curve2 will be the rectangle
apply washer.
this should work.

Answer 16

so the equation for the volume of a sphere - the volume of a cylinder? and @ polpak ? oh and calc 2

Answer 17

no

Answer 18

did what i just wrote make any sense?

Answer 19

lol i typed that before reading urs and yes it did i'll go ahead and try that ty :D

Answer 20

okay good luck
rotate about y axis!

cheers!