A child loves to watch as you fill a transparent plastic bottle with shampoo (se

Question

A child loves to watch as you fill a transparent plastic bottle with shampoo (see figure below). Every horizontal cross section of the bottle is circular, but the diameters of the circles have different values. You pour the brightly colored shampoo into the bottle at a constant rate of 15.0 cm3/s.

A child loves to watch as you fill a transparent plastic bottle with shampoo (see figure below). Every horizontal cross section of the bottle is circular, but the diameters of the circles have different values. You pour the brightly colored shampoo into the bottle at a constant rate of 15.0 cm3/s. At what rate is its level in the bottle rising at a point where the diameter of the bottle is d1 = 5.10 cm? At what rate is its level in the bottle rising at a point where the diameter of the bottle is d2 = 1.49 cm?

Explanation / Answer

a) dV/dt = A * dh/dt

A = pi r^2

dh/dt = 15/(pi*(5.1/2)^2)=0.734

b)dh/dt = 15/(pi*(1.49/2)^2)=8.60

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