Coffee Maker Cone Filter
Issues relating to fares! 10 POINTS!?
1. A conical paper cup (vertex down) is being filled with water at 3 cm ^ 3 times per second. If the depth of water is always twice the radius on the surface, we find the following: a) How fast is the radius increases when water is 2 inches deep How? [I have 3 / (2pi) cm / s] b) fast is the surface area increasing water when the water is 2 inches deep? [I -44.25 cm ² / sec, which can not be right] 2. A coffee machine has a filter holder and filter in the form of a cone with a radius of 5 cm. 500 cm ^ 3 of water poured into the filter holder. Brewed coffee drips out of the cone, at 20 cm ^ 3/min in a cylindrical coffee pot has the same radius as the filter holder. a) Find a formula for the rate of change of the depth of coffee in the coffee. b) What is the final depth of coffee in the coffee pot? Please show work, which helps the most gets 10 points!
1:. Since dV / dt = 3 cm ^ 3 / sh (t) = 2r (t) a.) h = 2 cm, r = V 1 cm (t) = 1 / 3 (pi) * h (t) * r (t) ^ 2 = 2pi * r ^ 3 dV / dt = 6PI ^ r * 2 (dr / dt) = 3 = 6PI (dr / dt) 3 = dr / dt = 1 / (2pi) cm / sb) A = pi * r ^ 2 dA / dt = 2pi * r * (dr / dt) dr / dt = 1 / (2pi) dA / dt = r = 1 cm ^ 2 / sec 2. Given dVcone / dt = -20 cm ^ dVcyl 3/min / dt = 20 cm ^ 3/min VCON R = 5 cm = 500 cm ^ 3 Vcyl = pi * r ^ 2 h = 25pih a.) dVcyl / dt = 25PI * (dh / dt) = 20 dh / dt = 4 / (5pi ) cm / min b) Vcyl = 25PI * H = 500 cm ^ 3 H = 20/pi cm
Orchid – single cup coffee maker – johnkwarner
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