### 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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