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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
 one year ago
 one year 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
 one year ago
 one year ago

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iop360Best ResponseYou've already chosen the best response.0
\[\frac{ dV }{ dt } = +2.9, \frac{ dH }{ dt }=?\]
 one year ago

ChlorophyllBest ResponseYou've already chosen the best response.1
@iop360 Do you have the Volume formula?
 one year ago

iop360Best ResponseYou've already chosen the best response.0
\[V = \frac{ 1 }{ 3 }(\pi)r^2h\]
 one year ago

ChlorophyllBest ResponseYou've already chosen the best response.1
No this one, have 2 bases!
 one year ago

iop360Best ResponseYou've already chosen the best response.0
i think what we are supposed to do though is make it into two cones though
 one year ago

iop360Best ResponseYou've already chosen the best response.0
b and B represent the different volumes?
 one year ago

iop360Best ResponseYou've already chosen the best response.0
how did you derive this formula
 one year ago

iop360Best ResponseYou've already chosen the best response.0
im getting a wrong answer
 one year ago

iop360Best ResponseYou've already chosen the best response.0
answer is supposed to be 10.3 cm/min
 one year ago

iop360Best ResponseYou've already chosen the best response.0
oh wait i think i made an error.. let me recalculate
 one year ago

iop360Best ResponseYou've already chosen the best response.0
my expression for V is: \[V = [\frac{ 16 }{ 27 }(\pi)h^3 + \frac{ 4}{ 27 }(\pi)h^3 + \frac{ 1 }{ 9 }(\pi)h^3]\]
 one year ago

iop360Best ResponseYou've already chosen the best response.0
oh wait.. 1/27, not 1/9
 one year ago

iop360Best ResponseYou've already chosen the best response.0
ok yeah thats what i get now
 one year ago

iop360Best ResponseYou've already chosen the best response.0
taking its derivative, you get \[\frac{ 7 }{ 3 }(\pi)h^2\]
 one year ago

iop360Best ResponseYou've already chosen the best response.0
dh/dt beside it of course
 one year ago

iop360Best ResponseYou've already chosen the best response.0
(2.9)/(7pi/3) = dh/dt after you plug h =1, which does nothing
 one year ago

iop360Best ResponseYou've already chosen the best response.0
i think we did it right, not sure why its resulting in the wrong answer
 one year ago

iop360Best ResponseYou've already chosen the best response.0
did you get 0.395...m/min
 one year ago

iop360Best ResponseYou've already chosen the best response.0
doesnt that still result in 39.5cm/min then?
 one year ago

iop360Best ResponseYou've already chosen the best response.0
try reading this http://www.askmehelpdesk.com/mathematics/relatedratesfrustumcone352086.html
 one year ago

iop360Best ResponseYou've already chosen the best response.0
it might be a solution, but i dont get it
 one year ago

iop360Best ResponseYou've already chosen the best response.0
hmm is there anything extra in the formula you may have forgotten
 one year ago

iop360Best ResponseYou've already chosen the best response.0
http://www.youtube.com/watch?v=1v1PplJSKY this video ?
 one year ago

iop360Best ResponseYou've already chosen the best response.0
http://jwilson.coe.uga.edu/emt725/Frustum/Frustum.cone.html this link doesnt have a square root in the formula
 one year ago

iop360Best ResponseYou've already chosen the best response.0
bleh, the formula without the sq.root doesnt work either...
 one year ago

iop360Best ResponseYou've already chosen the best response.0
forgot the pi from the above forumla
 one year ago

iop360Best ResponseYou've already chosen the best response.0
http://jwilson.coe.uga.edu/emt725/Frustum/Frustum.cone.html
 one year ago

iop360Best ResponseYou've already chosen the best response.0
i got 10.1 though...calculator didnt take exact values
 one year ago

iop360Best ResponseYou've already chosen the best response.0
\[V = \frac{ (\pi)h }{ 3 }[R^2 + Rr + r^2]\]
 one year ago

iop360Best ResponseYou've already chosen the best response.0
im going to calculate it again..
 one year ago

iop360Best ResponseYou've already chosen the best response.0
im getting 10.05... cm/min that is slightly off
 one year ago

iop360Best ResponseYou've already chosen the best response.0
im going to try it with different values
 one year ago

iop360Best ResponseYou've already chosen the best response.0
oh wait...i used base for r in that last formula
 one year ago

iop360Best ResponseYou've already chosen the best response.0
annnnnnd were back to 21pi/27 h^3
 one year ago

iop360Best ResponseYou've already chosen the best response.0
yeah, i accidently used the B/b for that forumla instead of R/r
 one year ago

iop360Best ResponseYou've already chosen the best response.0
and yet i got close to a right answer
 one year ago

iop360Best ResponseYou've already chosen the best response.0
do we sub in h = 1 or h =6? h = 1 is right isnt it?
 one year ago

ChlorophyllBest ResponseYou've already chosen the best response.1
Yes, we calculate the instant rate when h = 1
 one year ago

iop360Best ResponseYou've already chosen the best response.0
the other guy reading this question: are you doing this question?
 one year ago

iop360Best ResponseYou've already chosen the best response.0
i could switch the values for the question and try it again if you want, haha
 one year ago

iop360Best ResponseYou've already chosen the best response.0
a 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?
 one year ago

iop360Best ResponseYou've already chosen the best response.0
it could be a glitch with the thing, maybe.
 one year ago

iop360Best ResponseYou've already chosen the best response.0
ok, im pretty sure were doing it right. imma close this down
 one year ago

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

ChlorophyllBest ResponseYou've already chosen the best response.1
I'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
 one year ago

iop360Best 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?
 one year ago

ChlorophyllBest ResponseYou've already chosen the best response.1
Ratio R and H: ( R  8 )/ ( 98) = H/5 > R = ( H/5 ) + 8
 one year ago
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