A circular oil slick of uniform thickness is caused by a spill of 1 cubic meter of oil. The thickness of the oil is decreasing at the rate of 0.1 cm/hr as the slick spreads. (Note: 1 cm = 0.01 m.) At what rate is the radius of the slick increasing when the radius is 8 meters? (You can think of this oil slick as a very flat cylinder; its volume is given by V = r2h, where r is the radius and h is the height of this cylinder.)

Question

I need help finding the dr/dt only cause I already did the rest.

Answer 1

V= T*pi*R^2 , T is thickness

Noticew I didn't use your formula for volume.

dV/dt= PI*T*2R dr/dt+ PI*r^2 dT/dt
But dV/dt = 0 (there is no more oil).
so

dr/dt= r^2 / 2TR * dT/dt

so what is T when R=8m?

V=PI*r^2*T
T= 8m^3/(PI*64m^2)=1/PI*8 m

in cm...T=100/8PI= you do it.
now working all measurements in cm
dR/dt= r^2/2TR dt/dr
dr/dt= 800/[2(800/8PI)800] * .1cm/hr
check all that.
dr/dt should be in cm/hr

Answer 2

Answer is c .803 METERS

Answer 3

Best