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

`(1)/(12\pi^(2)  )` seconds pass

Explanation:

V=
`(4)/(3)\pi r^(3) = (4)/(3)\pi   ((1)/(2) )^(3)=(4)/(3)\pi   (1)/(8)=(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

`(2\pi^(3)  )/(1 sec) =((\pi )/(6) )/(x)`

x=
`((\pi )/(6) )/(2\pi^(3)  ) =(1)/(12\pi^(2) )sec`