Answer to Question #341566 in Calculus for marco

Question

Air is pumped into a spherical balloon at the rate of 100 cm3/s. How fast is the diameter increasing when the diameter is 10 cm? 

Answer 1

$V=4/3\pi r^3$

$r=0.5 D$

$V=4/3\pi (0.5D)^3=1/6 \pi D^3$

$dV/dt=1/2\pi D^2 dD/dt$

$dD/dt=(dV/dt)/(0.5\pi D^2)=100/(0.5(10)3.14)=6.37 cm/s$