Question

A spherical balloon centered at (2,1,2) starts at 1 cm in diameter and begins growing.The sphere is being inflated at a constant rate of2π3cm3/sec. How much time passes beforethe balloon touches the unit sphere?3

Answer 1

Answer:

$\frac{1}{12\pi^{2} }$ seconds pass

Step-by-step explanation:

V=$\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi (\frac{1}{2} )^{3}=\frac{4}{3}\pi \frac{1}{8}=\frac{1}{6}\pi cm^{3}$

(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 $2\pi ^{3} cm^{3} /s$

So

$\frac{2\pi^{3} }{1 sec} =\frac{\frac{\pi }{6} }{x}$

x=$\frac{\frac{\pi }{6} }{2\pi^{3} } =\frac{1}{12\pi^{2} }sec$