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iop360
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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
 2 years ago
 2 years ago
iop360 Group Title
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
 2 years ago

This Question is Closed

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

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
of a regular cone, yes
 2 years ago

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

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

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
dw:1353202550485:dw
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.0
R is top radius?
 2 years ago

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

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
ill try it. thanks!
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.0
have you tried it?
 2 years ago

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
i got .383...m/min
 2 years ago

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

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

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
what did you get?
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.0
oh wait.. 1/27, not 1/9
 2 years ago

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

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

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

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
0.395...m^3/min
 2 years ago

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

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

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

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

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

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

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

iop360 Group TitleBest 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
 2 years ago

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
!!! i think i got it
 2 years ago

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
http://jwilson.coe.uga.edu/emt725/Frustum/Frustum.cone.html
 2 years ago

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

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

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

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

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

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
ill try it with r/R
 2 years ago

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

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

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

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

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

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

Callisto Group TitleBest ResponseYou've already chosen the best response.0
*learning* ._.!
 2 years ago

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

iop360 Group TitleBest 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?
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.0
answer: 1.4cm/min
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.0
i get 1.9 ..hmmm
 2 years ago

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

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

iop360 Group TitleBest ResponseYou've already chosen the best response.0
thanks for the help
 2 years ago

Chlorophyll Group TitleBest 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 :)
 2 years ago

Chlorophyll Group TitleBest 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
 2 years ago

iop360 Group TitleBest 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?
 2 years ago

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