# Math

Corn is poured through a chute at the rate of 10ft^3 / min and falls in a conical pile whose bottom radius is always half the height. How fast is the circumference of the base changing when the pile is 8 feet high?

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1. h = 2r, so

v = 1/3 pi r^2 * 2r = 2pi/3 r^3

dv/dt = 2pi r^2 dr/dt
10 = 2pi*4^2 = 32pi dr/dt
dr/dt = 5/16pi

now, c = 2pi*r, so
dc/dt = 2pi dr/dt
= 2pi * 5/16pi = 10/16 = 5/8

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2. Pauline jogs at 5 1/3 miles per hour for 1 5/6 hours. about how many miles has she walked?

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