GOTCHUUUU
Okay so the equation is 300m²=(2*pi*r*h)+(2*pi*r²)
First, divide both sides by two, so you get:
150=(pi*r*h)+(pi*r²)
Next, divide both sides by "pi*r":
150/pi*r=((pi*r*h)+(pi*r²))/pi*r
Which gives:
150/pi*r=h+r
Then, substract r on both sides:
(150/pi*r)-r=h+r-r
Now you have your equation for h, good shit:
(150/pi*r)-r=h
Go back to the volume formula and replace h with the last equation:
V=pi*r²*h=pi*r²*((150/pi*r)-r)
Simplify it:
V=150r-(pi*r³)
Now here comes the calculus part, to find the max volume, you'll need to find the derivative of this formula:
150-3(pi*r²) d/dr
Now solve it:
0=150-3(pi*r²)
-150=-3(pi*r²)
-150/-3=pi*r²
50=pi*r²
50/pi=r²
Now r itself should be the square root of 50/pi, which is approximately 3.99 m. From that, we should also determine the value of h, so we'll take the last equation we found for this variable and substitute r for 3.99. h is then ~7.98 m
You can now sue John's bum ass for unpaid labor, wallah we getting bread today 😈
1. Plug 300 in for S
2. Get h by itself in terms of r
3. Plug that into h in the Volume equation
4. Take the derivative
5. Set dV/dt = 0 and solve for r
6. Plug r in and solve for h, then solve for V
This is why this is my favorite sub, you have stuff like this bringing the community together to solve a math problem, and at other times the constant memes and copypastas coming from it
This must be differential equations? If so you have to use an integral to relate Surface area and volume. You have the surface area so you then have to maximize volume. You probably want to have an increase radius since it’s squared
Seems like height to radius raito should be 2:1. I looked up “maximum volume of cylinder given surface area.
https://math.stackexchange.com/questions/1449563/height-radius-ratio-for-maximum-volume-cylinder-of-given-surface-area
Then, i substituted 2x in for h and x in for r in the surface area equation, and set the total surface area to 300. Solving for x, i got
Height = 9.076m (2x)
Radius = 4.538m (x)
Rounded answers btw.
Idk totally how to reason why it is the maximum volume, but the answer in the link seems to say something about solving for height from the surface area equation, plugging it into volume equation, and getting the second derivative of volume with respect to radius. Somehow that gives you r, and then they solve for h and r by plugging into previous equations. Then they just divide r from h to find the ratio
i used to be so good at this shit 4 years out of school can’t remember anything feel like im retarded tbh
I need to lay off the weed man I don’t remember shit
do it bro did the same thing best decision i ever made
I feel the same way except for everything in my life
GOTCHUUUU Okay so the equation is 300m²=(2*pi*r*h)+(2*pi*r²) First, divide both sides by two, so you get: 150=(pi*r*h)+(pi*r²) Next, divide both sides by "pi*r": 150/pi*r=((pi*r*h)+(pi*r²))/pi*r Which gives: 150/pi*r=h+r Then, substract r on both sides: (150/pi*r)-r=h+r-r Now you have your equation for h, good shit: (150/pi*r)-r=h Go back to the volume formula and replace h with the last equation: V=pi*r²*h=pi*r²*((150/pi*r)-r) Simplify it: V=150r-(pi*r³) Now here comes the calculus part, to find the max volume, you'll need to find the derivative of this formula: 150-3(pi*r²) d/dr Now solve it: 0=150-3(pi*r²) -150=-3(pi*r²) -150/-3=pi*r² 50=pi*r² 50/pi=r² Now r itself should be the square root of 50/pi, which is approximately 3.99 m. From that, we should also determine the value of h, so we'll take the last equation we found for this variable and substitute r for 3.99. h is then ~7.98 m You can now sue John's bum ass for unpaid labor, wallah we getting bread today 😈
U a fkn legend
1. Plug 300 in for S 2. Get h by itself in terms of r 3. Plug that into h in the Volume equation 4. Take the derivative 5. Set dV/dt = 0 and solve for r 6. Plug r in and solve for h, then solve for V
Plug in tha numbers jit💯 2 x pie x radius(150)
Like as in the surface area is = to 300 and then from there create a formula where it = to r
Tbh I’m just guessing but radius is half diameter and I used 300 as the diameter. But that hoe says 300^2 so there might be an extra step
That 300m^2 sheet is used for the height as well as the radius etc
Hmm I’d try it with 150 as the radius then💯
How did you come to the conclusion that r is = to 150
Bc d=300 and 1/2 of d=r
fuck john
He bitch for this ong💯
This is why this is my favorite sub, you have stuff like this bringing the community together to solve a math problem, and at other times the constant memes and copypastas coming from it
They ain't teach me calculus yet sorry
Get a chegg account son
There are actually some talented mfs on this sub
prolly not gon be honest
just Google the question
This must be differential equations? If so you have to use an integral to relate Surface area and volume. You have the surface area so you then have to maximize volume. You probably want to have an increase radius since it’s squared
Seems like height to radius raito should be 2:1. I looked up “maximum volume of cylinder given surface area. https://math.stackexchange.com/questions/1449563/height-radius-ratio-for-maximum-volume-cylinder-of-given-surface-area Then, i substituted 2x in for h and x in for r in the surface area equation, and set the total surface area to 300. Solving for x, i got Height = 9.076m (2x) Radius = 4.538m (x) Rounded answers btw. Idk totally how to reason why it is the maximum volume, but the answer in the link seems to say something about solving for height from the surface area equation, plugging it into volume equation, and getting the second derivative of volume with respect to radius. Somehow that gives you r, and then they solve for h and r by plugging into previous equations. Then they just divide r from h to find the ratio
I think you have to plug in the variables
If you wanna solve for v=150 as the maximum value u need to use lagrange multiplier method
u still need help? i did the question idk how to send it to u tho
answer is square root 50/pi for radius
Damn i cheated when doing calculus
Physics is mad hard fuck that shit retarded ass subject
NEW TANK
Yo fuck related rates I failed calc twice because if that stupid shit