Posted by **Liz** on Sunday, October 7, 2012 at 4:56pm.

grain is being poured through a chute at rate of 8 ft^3/min and forms a conical pile whose radius of the bottom is always 1/2 the height of pile. How fast is circumference increasing when the pile is 10 feet high?

- calculus -
**Reiny**, Sunday, October 7, 2012 at 7:40pm
given:

r = (1/2)h

2r = h

Let V be the volume

V = (1/3)π r^2 h

V = (1/3)π(r^2)(2r) = (2/3)π r^3

dV/dt = 2πr^2 dr/dt

when h = 10, r = 5

8 = 2π(25)dr/dt

dr/dt = 4/(25π)

Let circumference be C

C = 2πr

dC/dt = 2π dr/dt

so at that instance,

dC/dt = 2π(4/(25π) = 8/25 ft/min

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