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Sorry, I have no clue why the computer writes the equations this way but I'm pretty sure when there is a \ like for this exaple question question V=\frac{4}{3}\pi r^3 it is NOT a division sign I got confused on that for a sec so when it shows that before pi it doesn't mean divide by pi, just saying. Sorry for making you go through the trouble, but THANK YOU VERY MUCH for lookin into this and helping out, I really appreciate it!

The volume of a sphere is decreasing at a constant rate of 4635 cubic inches per second. At the instant when the radius of the sphere is 10 inches, what is the rate of change of the surface area of the sphere? The volume of a sphere can be found with the equation V=\frac{4}{3}\pi r^3 and the surface area can be found with S=4\pi r^2. Round your answer to three decimal places (if necessary).

Dec 8, 2020

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V = 4/3*pi*r^3

dV/dt = 4/3*pi*r^2

S = 4*pi*r^2

dS/dt = 8*pi*r

dr/dt = -4635

r = 10

dS/dt = 80

The rate of the change of the surface of the sphere is -80 in^3/sec.

Dec 8, 2020