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

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

\[\frac{ dV }{ dt } = +2.9, \frac{ dH }{ dt }=?\]
@iop360 Do you have the Volume formula?
of a regular cone, yes

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

\[V = \frac{ 1 }{ 3 }(\pi)r^2h\]
No this one, have 2 bases!
i think what we are supposed to do though is make it into two cones though
|dw:1353202550485:dw|
R is top radius?
b and B represent the different volumes?
how did you derive this formula
oh ok
ill try it. thanks!
hmm
have you tried it?
im getting a wrong answer
i got .383...m/min
answer is supposed to be 10.3 cm/min
oh wait i think i made an error.. let me recalculate
my expression for V is: \[V = [\frac{ 16 }{ 27 }(\pi)h^3 + \frac{ 4}{ 27 }(\pi)h^3 + \frac{ 1 }{ 9 }(\pi)h^3]\]
what did you get?
oh wait.. 1/27, not 1/9
ok yeah thats what i get now
taking its derivative, you get \[\frac{ 7 }{ 3 }(\pi)h^2\]
dh/dt beside it of course
(2.9)/(7pi/3) = dh/dt after you plug h =1, which does nothing
0.395...m^3/min
i think we did it right, not sure why its resulting in the wrong answer
did you get 0.395...m/min
doesnt that still result in 39.5cm/min then?
try reading this http://www.askmehelpdesk.com/mathematics/related-rates-frustum-cone-352086.html
it might be a solution, but i dont get it
hmm is there anything extra in the formula you may have forgotten
http://www.youtube.com/watch?v=1v1Pp-lJSKY this video ?
http://jwilson.coe.uga.edu/emt725/Frustum/Frustum.cone.html this link doesnt have a square root in the formula
bleh, the formula without the sq.root doesnt work either...
!!! i think i got it
forgot the pi from the above forumla
http://jwilson.coe.uga.edu/emt725/Frustum/Frustum.cone.html
i got 10.1 though...calculator didnt take exact values
\[V = \frac{ (\pi)h }{ 3 }[R^2 + Rr + r^2]\]
im going to calculate it again..
im getting 10.05... cm/min that is slightly off
hm ok
thanks
im going to try it with different values
oh wait...i used base for r in that last formula
uh oh
ill try it with r/R
annnnnnd were back to 21pi/27 h^3
yeah, i accidently used the B/b for that forumla instead of R/r
and yet i got close to a right answer
do we sub in h = 1 or h =6? h = 1 is right isnt it?
Yes, we calculate the instant rate when h = 1
the other guy reading this question: are you doing this question?
*learning* ._.!
i could switch the values for the question and try it again if you want, haha
ok i will
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?
answer: 1.4cm/min
alright
i get 1.9 ..hmmm
it could be a glitch with the thing, maybe.
ok, im pretty sure were doing it right. imma close this down
thanks for the help
Check with your teacher about the formula! I'll sure will message you if I find out something interesting :)
thanks!
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
thanks!
@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?
Ratio R and H: ( R - 8 )/ ( 9-8) = H/5 -> R = ( H/5 ) + 8

Not the answer you are looking for?

Search for more explanations.

Ask your own question