Answer:
Option C. [tex]r=20\ in[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex] ------> equation A
In this problem we have
[tex]r+h=30[/tex]
[tex]h=30-r[/tex] -----> equation B
substitute equation B in equation A
[tex]V=\frac{1}{3}\pi r^{2}(30-r)[/tex]
using a graphing tool
the largest possible volume for the sculpture is for [tex]r=20\ in[/tex]
see the attached figure
