Related Rates | Spheres Radius & Volume Test Question

Raw Transcript

Hello everybody this Is
Tom from EveryStepCalculus.com I’m gonna do a related rates
problem right off the internet and this
problem was the first when i searched
related rates for a sphere and related rates is always got some sort of formula
to it they deal with cones and
spheres and cylinders and
this one is a sphere so we’re going to get started index eight to go to my
calculus one menu and we’re gonna
you can go up or down on this, this scroll up there down by like to go up
if the
the letters are r there related rates which is closer it z than a
and wait for it to load here
and you can see this
arrow here and on any menu shows you that there’s more to it than that
they’re all in alphabetical order so sphere would be
in the s section here’s sphere
and in the problem that
was on the youtube your asked to find
dv/dt in other words how much is the volume changing
with the change in radius and so we’re going to choose number two
to do that and the radius rate that they give you
is 4 so we to enter anything into these entry lines on my program any of my
programs you have to press alpha
first alpha 4 and
the problem says its increasing we’re going to choose number two you can scroll to it
here or you can choose a number before it
I like to choose the number it’s quicker and it says per second we’re going to choose
that
and then it gives a diameter
so the radius but the formula is with radius so that needs to be converted
you give you a diameter the little tricks in calculus or physics they love the trick
you
and so the diameter is alpha
he gives an alpha of 80 and which is the radius of 40
divided by 2 and he gives millimeters
notice how many variables there are in this problem in other words millimeters
per second um, the
related rate for the radius and
change in volume so you you got many
things this one he gives millimeters
so we’re going to choose that I show you what you entered so you can change it if you want notice
millimeters cubed per second and the radius is millimeters then
have to be the same I say it’s okay
you write this all on your paper here’s the computation of the actual formula
within related rates in other words we’re taking the derivative
verses with respect to time to
of both sides of the equation there’s
v and here’s the right side and that turns into
4 pie r squared dr/dt then you add the variables here
and what comes up is 25600 pie
millimeters cubed per second now notice that
you would get 100% on this problem but if you had minutes you would have been
wrong if you had feet you’d be wrong et cetera so
the program catches all this stuff so you get a 100%
fabulous program one of the best I’ve written
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