Endless Paradigm

the volume of the sphere is calculated as
4/3*π*R^2

the volume of the bar is calculated as
π*(D/2)^2*L

how to find the volume of this cross section?

also I will probably need to figure out how to find the surface area of the spherical arc/curve/region that overlaps

You will find the answer.  Then you will pass the test.  Then you will never, ever, EVER, need the answer EVER again.

Volume of a generic sphere is:
V = ⁴/₃ π r³  (not squared)

Otherwise, wee can see that the intersection is a cut off portion of the sphere, the diameter of which is equal to a side depth of the bar.

Google shows me this: http://mathforum.org/dr.math/faq/formula...phere.html
Use the volume of the spherical cap.

I'm not quite sure how to isolate the height components in the formula though.

yeah that would be the problem... I assume there is probably a trig ratio for this somewhere

I've got it



you can use trig on the triangle
Pythagorean at the least

now to tackle the surface area issue

Nah, you'd just have to grab the height component and substitute it into the volume formula I'd imagine.

Actually, I think my algebra's comming back to me:
(where r₁ is the radius of the base)
r = (h² + r₁²)/(2h)
2hr = h² + r₁²
h² - 2hr + r₁² = 0

h = (2r ± √4r² - 4r₁²) / 2
= r ± √r² - r₁²

In this case, r > h, so the ± is probably a -

Plug h into volume formula:
V = (Pi/6)(3r₁² + h²)h

EDIT: I'm not sure your thing exactly works cause you're introducing more variables?

Think I got it