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April 16, 2014

April 16, 2014

Posted by **Yoona** on Tuesday, January 3, 2012 at 12:02am.

a. At the time when the radius of the sphere is 10 cm, what is the rate of increase of its volume?

b. At the time when the volume of the sphere is 36pi cubic centimeters, what is the rate of increase of the area of a cross section through the center of the sphere?

c. At the time when the volume and the radius of the sphere are increasing at the same numerical rate, what is the radius?

- calculus -
**Reiny**, Tuesday, January 3, 2012 at 9:44amdV/dt = 4πr^2 dr/dt

a) when r=10 and dr/dt = .04

dV/dt = 4π(100)(.04) = ...

b) when V = 36π

36π = (4/3)πr^3

27 = r^3

r = 3

cross section is a circle, A = πr^2

dA/dt = 2πr dr/dt

= 2π(3)(.04)

= ..

c) dV/dt = 4πr^2 dr/dt, but dr/dt = dV/dt = .04

.04 = 4πr^2 (.04)

4πr^2 = 1

r^2 = 1/(4π)

r = 1/(2√π) = ...

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