PLEASE HELP ME!!!! Please!!

Question

The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing (in mm³/s) when the diameter is 100 mm? (Round your answer to two decimal places.)

= ? mm^3/s

Answer 1

v = (4/3)pi(r)^3

v' =4pi(r^2)r'= 4pi(100/2)^2(3)= 12p(50)^2=2500(12pi)

= exactly 30,000pi mm^3/s

= about 94,247.78 mm^3/s

dV/dt=V'= 4pi(r^2)dr/dt= 4pi(50^2)(3)

df/dt=r'=3

r=d/2=100/2=50

pi=about 3.14159