Related rates (Lecture Part 5) Conical Tank Calculation

In this video, we calculate the rate of change of the water level in a tank that is the shape of an inverted cone. This video picks up where we left off in Part 4, where we have already found the formula needed that relates the rates of change of volume and height, dV/dt to dh/dt. It is an excerpt from a Calculus 1 lecture.

[stephaniagrauer]

Stephania Grauer
MAC2311
One important thing mentioned in the video is that feet squared would be for area and that feet cubed would be for volume.

[maxwelljakus]

Maxwell Jakus MAC2311 T/R 11:00 am - 1:15 pm - A part of this video I found helpful was the use of dV/dt and how it applies to volume.

[connorz]

Connor Zivitz
MAC2311 2-3:15 pm M-R
So we use a similar triangle proportion to replace the "r" term in the formula with (5/12)h, simplify and then differentiate.

[rileyfreemang]

Eric Haynes
MAC 2311
"10=100pi/9 dh/dt to solve for dh/dt multiply by 10 times 9/100pi" (Hearn 1:00-1:10)

[Learn--Code]

Michael Samuels
MAC 2311
Thank you for the video professor,
now that I have taken a second look on how to put together the formula for the volume =(1/3(pi)(r^2)h its a bit easier from there on.

[usmcdd]

Rocky Rosado
MAC2311
" we have ten equals 25 times 64 over 144 PI DH/DT all right so what we have is ten equals 100 PI over nine DH/DT to solve for DH/DT we just have to multiply ten times nine over 100 pi okay the ten  goes into 100 ten times and so we're gonna have 9/10 pi 0.286" (Hearn 00:45-01:18)

[paulchavez]

Paul Chavez
MAC 2311 2pm-3:15pm m-r
"to find dh/dt we are going to have to plug in the values found H and dv/dt"

[victoriasueropagan]

Victoria Suero
MAC2311 M-R
"so 8 squared dh/dt is what were are looking for, dv/dt is equal to 10 cubic feet per minute simplifying a bit..." (0:35-0:47)

[thethe]

Johnathan Spaulding
MAC2311 M-R
"for dh dt we just have to multiply 10 times 9 over 100 pi"

[alexandermarcelo]

alexander espinosa
MAC2311
after finding a relationship between dv/dt and dh/dt in the previous video, all of the values had to be plugged in to find dh/dt

[mohammadabid]

Mohammad Abid
MAC2311 M-R
"Only now that we have this formula relating dv/dt to dh/dt that describes the relationship between the rates at any time can we then plug in values for a particular moment in time."

[MyGamer]

Fathin Hossain
MAC2311, M-R 2pm
"Only now, that we have this formula relating dv/dt to dh/dt that describes the relationship between the rates at any time, can we then plug in values for a particular moment in time."

[justin_credible]

Justin Quarless
MAC2311
One important concept in the video was that we must have a formula describing the relation of rates before we can plug in values at a particular moment in time.

[shaneadelakun]

Shane Adelakun
MAC 2311
"to solve for the dhdt we just have to multiply 10 times 9 over 100 pi okay the 10 goes into 100 10 times"

[mstriker]

Mitchell Thanath
MAC2311 M-R
"height is linear, its not feet squared, its not feet cubed, feet squared would be for area, feet cubed would be for volume"

[queenkay]

Calecia
MAC2311 TR11am
One important thing in this video was pointing out that only until you have the formula relating the rates of dV/dt to dh/dt at anytime, then we can plug in values for a certain moment in time.

[vsim]

Vivica Simmons
MAC2311 M-R
"so we have dv/dt is equal to 25 over 144pi"

[roylope]

Royce Lopez
MAC 2311
"And so we are gonna have 9/(10pi)." (Hearn, 1:17)

[juantomasini]

MAC2311
“The formula dv/dt describe the relationship between the rates”