coffee filter holder 2
Related Questions Rates! 10 points!?
1. A conical paper cup (top down) is filled with water at a rate of 3 cm ^ 3/sec. If depth Water is always twice the radius to the surface, find the following: a) How fast is the radius increases when the water is 2 cm deep? [I 3 / (2 pi) cm / sec] b) How fast is the surface area of water increases when the water is 2 inches deep? [I am -44.25 cm ² / sec, which can not be right] 2. A coffee machine has a filter holder filter in the form of a cone with a radius of 5 cm. 500 cm ^ 3 of water spilled into the filter holder. Brewed coffee drips out of the membrane at a rate of 20 cm ^ 3/min in a cylindrical coffee pot has the same radius as the holder. a) Find a formula for the rate of change of the depth of coffee in the coffeemaker. b) What is the final depth of coffee the coffee pot? Please show work, that helps the most gets 10 points!
1. Given: dv / dt = 3 cm ^ 3 m / s (t) = 2r (t) a.) h = 2 cm, r = 1 cm V (t) = 1 / 3 (pi) * h (t) * r (t) ^ 2 = 2 pi * r ^ 3 dV / dt = r * ^ 6ft 2 (dr / dt) 3 = 6ft (dr / dt) 3 = dr / dt = 1 / (2 pi) cm / s b.) A = pi * r ^ 2 dA / dt = 2pi * r * (dr / dt) dr / dt = 1 / (2 pi) dA / dt = r = 1 cm ^ 2 / 2 sec. Given: dVcone / dt = -20 cm 3/min dVcyl ^ / dt = 20 cm ^ 3/min R = 5 cm = 500 cm ^ 3 Vcyl VCON = r * ft ^ 2h = 25pih a.) dVcyl / dt = 25ft * (dh / dt) = 20 dh / dt = 4 / (5 ') cm / min b.) Vcyl = 25ft * H = 500 cm ^ 3 H = 20/pi cm
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