Question

Use differentials to approximate the volume of material needed to make a rubber ball if the radius of the hollow inner core is 2 in., and the thickness of the rubber is 1/8 in.

Answer 1

$t=2 \space in$

$\sigma_c=500 Mpa$

$\tau=200 Mpa$

Solution:

as we know that 

$\sigma_c\times A_c = \tau\times A_s$

$\sigma_c\times\pi/4 D^2=\tau\times\pi D t$

$500/4 (D)= 200\times 10$

$D= 16 mm$