A soccer ball made of leather 1/8 in thick has an inner diameter of 8.5 in . Use the formula V=(4/3)πr 3 to calculate the volume. Model the ball as a hollow sphere and estimate the volume of its leather shell. Find dV = in^3

Question

unknownrandom · Answer

I can't wrap my head around this problem. I don't understand why you can't just find the surface area since the leather portion of the ball is the outer part.

md152727 · Answer

First you calculate the external volume of the ball. 
In the formula, you make r = 4.25 + 0.125 = 4.375 in 

Then you calculate the inner volume with the same formula, taking 4.25 in for the radius 

Now, you make the difference betwee external and internal volume, and you get the volume of the shell. 

(4/3)*pi*(4.375)^3 - (4/3)*pi*(4.25)^3 = (4/3)*pi*[(4.375)^3 - (4.25)^3] 

I let you make the calculations... 

Bye !

phi · Answer

They may want you to find the volume at r= 4.25
then use implicit differentiation to find dV as a function of dr
and plug in dr= 1/8 inch to *estimate* the volume of the "shell"

unknownrandom · Answer

@phi I believe this is what they want me to do. So would I do$$dV=\frac{ 4 }{ 3 }*3(4.25)^{2}*\pi*\frac{ 1 }{ 8 }$$

unknownrandom · Answer

That was right. Thank you for your help @phi!