A little girl buys a spherical balloon of total volume 1 cubic foot. She starts blowing to fill the balloon at a rate of .1 cubic feet per minute. How fast is the radius of the balloon increasing when she has the ballon halfway blown up?
A.
B.
C.
D.
The relationship between radius and volume for a sphere of radius
r is
, so we differentiate implicitly with respect to
t to get the relationship for the rates
. The balloon is half full (one half of a cubic foot) when
, which we solve to get
, and we have that
so we have
which we solve to get
