A spherical balloon is inflated so that its volume is increasing at the rate of 2 ft3/min. How rapidly is the diameter of the ba
lloon increasing when the diameter is 1.7 feet?
1 answer:
According to the question requirements
v= 4/3*pi*r^3
dv/dt = 4*pi*r^2*dr/dt
when
d= 1.7
r= 0.85
and
dv/dt = 2
2= 4*pi*(0.85)^2*dr/dtthus the the speed of increasing of the balloon's diameter is
dr/dt = 1/(2pi*(0.85)^2)
=<span>0.2203 ft/min</span>
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