Related Rates (Lecture Part 6) Rate of change of radius of sphere

In this related rates example, an excerpt of a Calculus 1 lecture, we discuss how to find the rate of change of a radius of a sphere when the radius is a particular size. The rate of change of the volume is constant.

[maxwelljakus]

Maxwell Jakus MAC2311 T/R 11:00 am - 1: 15 pm - An insight that I gained from watching this video was what different variable mean and how they relate to the word problem.

[stephaniagrauer]

Stephania Grauer
MAC2311
One important thing I learned from this video is that dr/dt refers to how fast the radius is changing.

[juantomasini]

Mac2311
The formula for volume of a sphere is v=(4pi/3)R^3

[justin_credible]

Justin Quarless
MAC2311
An insight I gained from watching this video was the importance of visualizing units. In this example dv/dt is cm^3/min, and dr/dt is cm/min.

[rileyfreemang]

Eric Haynes
MAC 2311
"take the derivative with respect of t the left side and the derivative of t of the right side d/dt(V)=d/dt(4/3pir^3)" (Hearn 1:45-1:52)

[victoriasueropagan]

Victoria Suero
MAC2311 M-R
"now remember 4/3pi are coefficients, we don't have to do anything with those, they just stay the same..." (1:55)

[mohammadabid]

Mohammad Abid
MAC2311 M-R
"One hint here is that we're talking about cubic centimeters which is a measure of volume so this is the rate of change of the volume with respect to time. In this case, they are telling us that dv/dt is 800 cubic centimeters per minute consistently."

[Learn--Code]

Michael Samuels
MAC 2311
Thank you for the video professor,
the most difficult part for me is coming up with the formula (dv/dt=4(pi)r^2(dr/dt) but with a little reasoning its possible.

[roylope]

Royce Lopez
MAC 2311
"So we have dv/dt=4pi(r)squared dr/dt." (Hearn, 2:22)

[queenkay]

Calecia
MAC2311 TR11am
A part of the video I found helpful was bringing the 4/3 pi out of the brackets and finding d/dt (r^3).

[paulchavez]

Paul Chavez
MAC 2311 2pm-3:15pm m-r
"we need to fin how fast the radius of the balloon is increasing so we need the relationship between dv/dt and dr/dt"

[vsim]

Vivica Simmons
MAC 2311 M-R
"dr/dt equals we don't know what and we are given what dv/dt is"

[mstriker]

Mitchell Thanath
MAC 2311 M-R
"We have the relationship between v and r so we are going to differentiate, so we're going to take the derivative with respect to t of the left side and the derivative with respect to t of the right side"

[shaneadelakun]

Shane Adelakun
MAC 2311
"we need the relationship between dvdt and drdt, we have the relationship between v and r so we're going to differentiate"

[alexandermarcelo]

alexander espinosa
MAC2311
to be able to solve this equation, it is important to know what the formula is for finding the volume of a sphere is.

[usmcdd]

Rocky Rosado
MAC2311
"So we have DV/DT is equal to 4pi*r^2*dr/dt"(Hearns 2:21-2:25)

[thethe]

Johnathan Spaulding
MAC2311 M-R
"they're telling us that dv dt is eight hundred cubic centimeters for a minute"

[MyGamer]

Fathin Hossain
MAC2311, M-R 2pm
"dr/dt = how fast the radius is changing."