Answer to Question #98759 in Calculus for hannah

Question #98759
Air is being pumped into a spherical ballon at a rate of 10cm^3/min. Determine the rate at which the radius of the ballon is increasing when the radius of the ballon is 20cm
1
Expert's answer
2019-11-15T13:17:29-0500

The volume of the ball is calculated by the formula V=4πr33V=\frac {4\pi r^{3}} {3}

The rate of change of volume is V˙=4πr2r˙\dot{V}=4\pi r^2 \dot{r}

Thus, r˙=V˙4πr2=(10cm3/min)/(4π(20cm)2)=\dot{r}=\frac{\dot{V} }{4\pi r^2}=(10 cm^3/min)/(4\pi (20cm)^2)= 0.00198943678864869169711104704216 cm/min




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