Answer:
[tex]\frac{1}{12\pi^{2} }[/tex] seconds pass
Step-by-step explanation:
V=[tex]\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi (\frac{1}{2} )^{3}=\frac{4}{3}\pi \frac{1}{8}=\frac{1}{6}\pi cm^{3}[/tex]
(Volume of the D=1 cm sphere)
Now we have to find out the time needed to reach that volume at the filling rate of [tex]2\pi ^{3} cm^{3} /s[/tex]
So
[tex]\frac{2\pi^{3} }{1 sec} =\frac{\frac{\pi }{6} }{x}[/tex]
x=[tex]\frac{\frac{\pi }{6} }{2\pi^{3} } =\frac{1}{12\pi^{2} }sec[/tex]
