I'm trying to solve this problem, but I don't know how to set up the problem:
A golf ball consists of a spherical cover over a solid core. Let "t" denote the thickness of the cover and "r" denote the radius of the core.
a) Determine a formula for the exact volume of the cover
b) Use differentials to approximate the volume of the cover at "r"
c) If r = 0.8 inches and t = 0.04 inches, determine the exact volume of the cover
d) If r = 0.8 inches and t = 0.04 inches, approximate the volume of the cover
e) Compute the error ( true value - approximate value)
f) Compute relative error (error/actual value)
I know it seems like a lot to ask for, and I'm not asking for the answers, or all of the answers; I just need some help so that I can work through the problem.
Thank you in advance.
I don't understand what part b is trying to ask for. As far as I know, when there is a problem involving differentials, I use the linear approximation formula. I think I'm having issues with the variables.
For b, if I'm approximating the volume of the cover, wouldn't I be using the formula from part a, then take the derivative?
Side note:
I asked my professor for some help, and she told me that the volume of the cover, which can be called f, will be the difference of the volume of the two concentric spheres. She also menioned that f = ΔV, where V is the volume of a sphere of radius r, which would be the sphere on the inside. She told me to approximate f, not V.
This confuses me more.
the first formula gets you the exact volume of the cover, the differential equation approximates it
Differentials and volume - YouTube
(b) ... the differential, , is the approximation for for the volume of the cover.
I just put the numbers given in parts (c) and (d) to show you how the approximation works. If you put the same numbers in the equation written for part (a), that gets you the exact volume of the cover.
calculate both, then finish (e) and (f).
I might come off as sounding hard-headed, but I and getting confused with what you're telling me and what my professor told me.
she told me that the volume of the cover, which can be called f, will be the difference of the volume of the two concentric spheres. She also menioned that f = ΔV, where V is the volume of a sphere of radius r, which would be the sphere on the inside. She told me to approximate f, not V.