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1986318 No.1986318 [Reply] [Original]

I'm having such a hard time with my Calc class right now...
can anyone offer me some help?

I'm trying to optimize the shape of a cylinder with the given Volume of 1000cm^3,
now i'm not asking for you guys to do my homework for me, just a little bit of help, or a push in the right direction would be awesome.

>> No.1986322

My Calc teacher always gave us the following hint:

"If you're completely unsure of what to do, take the derivative of whatever you got. If you're still unsure, set it to zero."

You'd be surprised how many Calc problems are solved in this same way.

>> No.1986323

By optimize it I assume you mean minimize surface area.
Find an equation for the surface area of the cylinder in terms of the radius, then find the minimum of that equation by setting the derivative equal to zero.

>> No.1986327

maximize the shape? height? or radius? shape is not quantifiable.

>> No.1986329

>>1986323
already did that,

my first step is finding out the surface area of a cylinder.
which is 2πrh+2πr^2

now how do i connect the volume to the surface area, do i put r in terms of h?

>> No.1986333

>>1986327
i apologize,
i meant minimize the surface area of a cylinder, because i'm tying it into a cost equation later.

>> No.1986340

V=(pi*r^2)*h
SA=2pi*r^2+2pi*r*h

take derivatives, set equal to zero.

>> No.1986344

>>1986329
Well the equation for the volume is just πr^2h, and you know that's equal to 1000.

>> No.1986346

>>1986340
>>1986340

hint: implicit differentiation, implicit differentiation everywhere.

>> No.1986352

>>1986340
i'm thinking that for the surface area aspect, i'm gonna have to get it down to one variable first,

so with the equation 2πrh+2πr^2, i'm gonna make that h into terms of r, so that i can effectively take the derivative of it.

>> No.1986385

>>1986352
nevermind, i'm dumb.

i took the volume equation

1000=πr²h and isolated h so that

h = 1000/(πr²)

and plugged that into the surface area equation for the variable "h":

f(x) = 2πr(1000/πr²) + 2πr²

>> No.1986670

so anyways, the answers for the height and radius in cm is

h = 10.83

r = 5.42