The volume of a spherical object is given by V= (4 pi)/(3) r^ 3 . How fast is the volume changing at the moment that the radius is 10 mm and increasing at a rate of 0.8 (mm)/(day)

Question

Help me answer this question please

Answer 1

dV/dt = dV/dr * dr/dt

r = 10 mm

dr/dt = .8 mm/day

If V = 4/3 πr³, dV/dr = 4πr² Note that this is the formula for the surface area of a sphere.

(If you do this calculation with the area of a circle, you get the circumference_.

Thus, dV/dt = dV/dr dr/dt = 4πr² dr/dt = 4 π * 10² * 8 = 3200π mm³ / day