A child loves to watch as you fill a transparent plastic bottle with shampoo. Ev

Question

A child loves to watch as you fill a transparent plastic bottle with shampoo. Every horizontal cross-section of the bottle is a circle, but the diameters of the circles all have different values, so that the bottle is much wider in some places than in others. You pour in bright green shampoo with constant volume flow rate 18.0cm3/s. At what rate is its level in the bottle rising at a point where the diameter of the bottle is 6.60cm? At what rate is its level in the bottle rising at a point where the diameter is 1.38cm?

Explanation / Answer

a)

A=pid^2/4 =pi*(0.066)^2/4 =34.2 cm ^2

dV/dt =A(dh/dt)

18 =34.2 *(dh/dt)

dh/dt =0.526 cm/s

b)

A=pi*1.38^2/4 =1.5 cm^2

dh/dt =18/1.5

dh/dt =12.03 cm/s

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