Answer to Question #336374 in Calculus for John

Question #336374

Related Rates: Problem Solving


Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.


Sand is being dropped at a rate of 10 cubic feet per minute onto a conical pile. If

the height of the pile is always twice the base radius, at what rate is the height

increasing when the pile is 8 feet high?


PLEASE ANSWER MY QUESTION QUICKLY!!

DEADLINE : 05/03/2022 11 : 00 PM




1
Expert's answer
2022-05-08T13:41:41-0400
V=13πr2hV=\dfrac{1}{3}\pi r^2h

Given h=2rh=2r


V=π12h3V=\dfrac{\pi}{12}h^3

Differentiate both sides with respect to tt


dVdt=π4h2(dhdt)\dfrac{dV}{dt}=\dfrac{\pi}{4}h^2(\dfrac{dh}{dt})

Then


dhdt=4πh2(dVdt)\dfrac{dh}{dt}=\dfrac{4}{\pi h^2}(\dfrac{dV}{dt})

When the pile is 8 feet high


dhdt=4π(8ft)2(10ft3/min)\dfrac{dh}{dt}=\dfrac{4}{\pi (8ft)^2}(10{ft}^3/min)

=58πft/min0.199ft/min=\dfrac{5}{8\pi}ft/min\approx0.199ft/min

The height is increasing at rate of 0.199 feet per minute when the pile is 8 feet high.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment