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anonymous
 one year ago
I need Calculus help!!!
a conical paper cup is 15 cm high and has a radius of 5 cm the water level is rising at 4 cm/s. how quickly is the water being poured into the cup when the water is 8 cm deep?
in pi form with cm^3/s.
anonymous
 one year ago
I need Calculus help!!! a conical paper cup is 15 cm high and has a radius of 5 cm the water level is rising at 4 cm/s. how quickly is the water being poured into the cup when the water is 8 cm deep? in pi form with cm^3/s.

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madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.0Let h represent the height of the water in the cup, r the radius of the circular top of the water level, and V the volume of water in the cup. The ratio of radius over height is constant for cones with the same angle, so because the paper cup has radius 3 cm and height 10 cm, the ratio r/h is equal to 3 cm over 10 cm, or r/h = 3/10. This gives us that r = 3/10 · h. Now we can relate the volume of water in the cup to the height and radius by the equation for the volume of a cone, V = (1/3)πr2h. In particular, using our equation for r in terms of h, this gives us V(t)=(1/3)pi*· (3/10 · h(t))^2*h(t)=(3pi/100)*h(t)^3 Using implicit differentiation on this relation gives us V(t)=(9pi/100)*h(t)^2h'(t), h'(t)=V'(t)/(9pi/100)*h(t)^2 When h(t) = 5 cm, the rate of change of volume is of course V (t) = 2 cm3/s (since this value is constant), so substituting these values into the above relation tells us that the water level is rising at a rate of h (t) = 8/(9π) cm/s.

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.0listen this is the solution of a sum i had ...but both these sums are same only the numbers are different

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.0you put your numbers in the correct place and you'll get your answer

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.0A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is poured into the cup at a rate of 2 cm3/s, how fast is the water level rising when the water is 5 cm deep? this is the question which i have solved...probably it will help you

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.0hey did you get it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes thank you so much!

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.0your most welcome
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