Answer to Question #98760 in Calculus for hannah

Question

air is being pumped into a spherical balloon at a rate of 10cm^3/min. Determine the rate at which the radius of the balloon is increasing when the radius of the balloon is 20 cm

Answer 1

$V=(4/3)πR^3$

Differentiate w.r.t. t

$\frac{dV}{dt}=(4/3)π3R^2 \frac{dR}{dt}$

$\frac{dV}{dt}=4πR^2 \frac{dR}{dt}$

Given that,

$\frac{dV}{dt}=10cm^3/second$

$R=20cm$

$10=4π(20)^2 \frac{dR}{dt}$

$\frac{dR}{dt}=\frac{10}{4 \pi \cdot (20)^2}=0.0019cm/second$