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 2 years ago
A large container has the shape of a frustum of a cone with top radius 8m, bottom radius 2m, and height 6m. The container is being filled with water at the constant rate of 2.9m^3/min. At what rate is the level of water rising at the instant the water is 1m deep?
Answer: 10.3cm/min
 2 years ago
A large container has the shape of a frustum of a cone with top radius 8m, bottom radius 2m, and height 6m. The container is being filled with water at the constant rate of 2.9m^3/min. At what rate is the level of water rising at the instant the water is 1m deep? Answer: 10.3cm/min

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iop360
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ dV }{ dt } = +2.9, \frac{ dH }{ dt }=?\]

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1@iop360 Do you have the Volume formula?

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0\[V = \frac{ 1 }{ 3 }(\pi)r^2h\]

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1No this one, have 2 bases!

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0i think what we are supposed to do though is make it into two cones though

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0b and B represent the different volumes?

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0how did you derive this formula

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0im getting a wrong answer

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0answer is supposed to be 10.3 cm/min

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait i think i made an error.. let me recalculate

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0my expression for V is: \[V = [\frac{ 16 }{ 27 }(\pi)h^3 + \frac{ 4}{ 27 }(\pi)h^3 + \frac{ 1 }{ 9 }(\pi)h^3]\]

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0ok yeah thats what i get now

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0taking its derivative, you get \[\frac{ 7 }{ 3 }(\pi)h^2\]

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0dh/dt beside it of course

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0(2.9)/(7pi/3) = dh/dt after you plug h =1, which does nothing

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0i think we did it right, not sure why its resulting in the wrong answer

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0did you get 0.395...m/min

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0doesnt that still result in 39.5cm/min then?

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0try reading this http://www.askmehelpdesk.com/mathematics/relatedratesfrustumcone352086.html

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0it might be a solution, but i dont get it

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0hmm is there anything extra in the formula you may have forgotten

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.youtube.com/watch?v=1v1PplJSKY this video ?

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0http://jwilson.coe.uga.edu/emt725/Frustum/Frustum.cone.html this link doesnt have a square root in the formula

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0bleh, the formula without the sq.root doesnt work either...

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0forgot the pi from the above forumla

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0i got 10.1 though...calculator didnt take exact values

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0\[V = \frac{ (\pi)h }{ 3 }[R^2 + Rr + r^2]\]

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0im going to calculate it again..

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0im getting 10.05... cm/min that is slightly off

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0im going to try it with different values

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait...i used base for r in that last formula

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0annnnnnd were back to 21pi/27 h^3

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0yeah, i accidently used the B/b for that forumla instead of R/r

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0and yet i got close to a right answer

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0do we sub in h = 1 or h =6? h = 1 is right isnt it?

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, we calculate the instant rate when h = 1

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0the other guy reading this question: are you doing this question?

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0i could switch the values for the question and try it again if you want, haha

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0a large container has the shape of a frustum of a cone with top radius 10m, bottom radius 6m, and height 4m. The container is being filled with water at the constant rate of 2.9m^3/min. At what rate is the level of water rising at the instant rate the water is 2m deep?

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0it could be a glitch with the thing, maybe.

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0ok, im pretty sure were doing it right. imma close this down

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1Check with your teacher about the formula! I'll sure will message you if I find out something interesting :)

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1I'm so sorry that I'm underestimate this Related Rate frustum of Cone! Here's the correct logic: V = π/ 3 ( R² + Rr + r² ) H With r = 2 and R is Radius variable and H is the Height variable > V = π/ 3 ( R² + 2R+ 4 ) H ( 1 ) From the ratio of right triangle: ( R  2 ) / ( 8  2 ) = H/ 6 > R = H + 2 (2) Plug (2) into (1): => V = π/ 3 [ ( H +2) + 2( H +2) + 4 ] H = π/ 3 [ H³ + 6H² + 12H ] so V' = π/ 3 [ 3H² + 12H + 12 ] H' At H = 1: V' = 27 π/ 3 * H' 2.9 = 9 π * H' Thus H' = 2.9 / 9π = .1025 m/ min = 10.3 cm/ min

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0@Chlorophyll one question though.. what do you do exactly during the ratios of the triangle part? eg. say my top radius was 9, bottom was 8, and height was 5 how do you set it up exactly?

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.1Ratio R and H: ( R  8 )/ ( 98) = H/5 > R = ( H/5 ) + 8
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