Start with the formulas for the volumes of the sphere and cyl. respectively:
Vs = (4/3)*pi*r^3 Vc = pi*r^2*h
Here, sphere and cyl. have the same radius and height. Thus, the diam. of the sphere, d = 2r, has the same value as does h.
Thus, Vs = (4/3)*pi*r^3 and Vc = pi*r^2*(2r) = 50. Thus, pi*r^3 = 50, or
r^3 = 50/pi
Then Vs = (4/3)(pi)*(50/pi) = 200/3 ft^3
Unfortunately, this doesn't agree with any of the answer choices, 'though it's close to given choice 100/3 ft^3, off by a factor of 2.
The trick here is to eliminate variables (especially the cyl. ht., h) and to make appropriate substitutions.
