Asked by Anonymous
Sand falls from a conveyor belt at the rate of 20 m^3/min. The sand forms a conical pile where the height of the cone is always 4 times the radius. How fast is the radius changing when the pile is 4 meters high?
Answers
Answered by
Reiny
volume of cone
= V = (1/3)π r^2 h, but we know h = 4r or r = h/4
V = (1/3)π (h^2/16)(h)
= (1/48)π h^3
dV = (1/16)π r^2 dr/dt
when h = 4, r = 1
20 = (1/16)π(1) dr/dt
dr/dt = 320/π m/min
check my arithmetic, did it on the screen instead of writing it out first
= V = (1/3)π r^2 h, but we know h = 4r or r = h/4
V = (1/3)π (h^2/16)(h)
= (1/48)π h^3
dV = (1/16)π r^2 dr/dt
when h = 4, r = 1
20 = (1/16)π(1) dr/dt
dr/dt = 320/π m/min
check my arithmetic, did it on the screen instead of writing it out first
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.