Question

the radius r of a sphere is 4cm and is increasing at the rate of 0.5cm . At what rate is the volume?​

Answer 1

32π or 100.53 cm^3 to the nearest hundredth.

Explanation:

dr/dt = 0.5

V = (4/3)π r^3

So dV/dr = (4/3)* 3 π r^(3-1)

= 4πr^2

Rate of increase in volume:

dV/dt = dV/dr * dr/dt

At r = 4:

Rate of increase in Volume

dV/dt = 4π(4)^2 * 0.5

= 64π * 0.5

= 32π.