Answer to Question #336375 in Calculus for John

Question #336375

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.


A spherical snow ball is made so that its volume is increasing at a rate of 8 cubic

feet per minute. Find the rate at which the radius is increasing when the snowball

is 4 feet in diameter.


PLEASE ANSWER MY QUESTION QUICKLY!!

DEADLINE : 05/03/2022 11 : 00 PM




1
Expert's answer
2022-05-09T11:06:19-0400
V=43πR3V=\dfrac{4}{3}\pi R^3

Differentiate both sides with respect to tt

dVdt=4π3(3R2)(dRdt)\dfrac{dV}{dt}=\dfrac{4\pi}{3}(3R^2)(\dfrac{dR}{dt})

Then


dRdt=14πR2(dVdt)\dfrac{dR}{dt}=\dfrac{1}{4\pi R^2}(\dfrac{dV}{dt})

Given dVdt=8ft3/min,D=4ft.\dfrac{dV}{dt}=8{ft}^3/min, D=4ft.

dRdt=14π(4ft/2)2(8ft3/min)=12πft/min\dfrac{dR}{dt}=\dfrac{1}{4\pi (4ft/2)^2}(8{ft}^3/min)=\dfrac{1}{2\pi}ft/min0.159ft/min\approx0.159 ft/min

The radius is increasing at rate of 0.159 feet per minute when the diameter is 4 feet.



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