Volume：The radius r of a sphere is increasing at a rate of 2 inches per minuteFind the rate of change of the volume when r=6 inches and r=24 inchesExplain why the rate of change of the volume of the sphere is not constant even though dr/dt is const

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Volume：Theradiusrofasphereisincreasingatarateof2inchesperminuteFindtherateofchangeofthevolumewhenr=6

Volume：The radius r of a sphere is increasing at a rate of 2 inches per minuteFind the rate of change of the volume when r=6 inches and r=24 inchesExplain why the rate of change of the volume of the sphere is not constant even though dr/dt is const
Volume：The radius r of a sphere is increasing at a rate of 2 inches per minute
Find the rate of change of the volume when r=6 inches and r=24 inches
Explain why the rate of change of the volume of the sphere is not constant even though dr/dt is constant

Volume：The radius r of a sphere is increasing at a rate of 2 inches per minuteFind the rate of change of the volume when r=6 inches and r=24 inchesExplain why the rate of change of the volume of the sphere is not constant even though dr/dt is const
V=Volume=4π(r^3)/3,dV/dr=4π(r^2),
so the rate of change of the volume, dV/dt=(dV/dr)*(dr/dt)=4π(r^2)*2,
then you can calculate the value of dV/dt is 288 square inch per minute when r=6 inches,and 4608 square inch per minute when r=24 inches.
The rate changes because it is related to both dr/dt and dV/dr, the latter of which is not constant.

V~R^3~T^3

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