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A candy company needs a custom box for their truffles. The box they've chosen is in the shape of a cylinder with a hemisphere of the same radius on top. The total volume of the box is V= 1/2(4r^2pi/3) + r^2pi(y-r), where y is the height of the box and r is the radius. Originally the candy box was designed to have a height of 6 inches and a radius of 2, but the shipper suggests that the boxes be made slightly shorter. You now need to adjust the radius so that the height is reduced to 5.75 but the volume remains constant. A. Find the value of dr/dy at the point r =2, r = 6. Help with process
Just need help getting started.
mertsj would be surprised if I solved this
Why is that? I really don't understand how dy/dr can be taken on that formula. I'll write it out nicer if you like.
\[1/2(4\pi r^2\div 3)+\pi r^2(y-r)=V\]
Okay, I got it
Thanks a lot. Let me know if you need anything else.
r = 2, y = 6, right?
Later they ask you to use your dr/dy to change the radius to 5.75.
-3/11 = dr/dy
Hero, thank you, but this is free response and I needed help with the process.
Can anyone help me with the process?
Maybe. Do you know how to take the derivative of Volume?
Yes. Typically though, it is d/dt. That is what is tripping me up. This time it is dr/dy. What changes?
derivative of the radius with respect to y, rather than t
So, when you end up taking the derivative of an 'y' values, you get dr/dy? ex. dr/dy(2y^2) = 4y dr/dy?
I suppose my question is this: What happens mathematically when you take the derivative of radius in respect to height?
Well, it doesn't exactly work like that but you're on the right track. If you have an expression with y and you take the derivative of r with respect to y, you take the derivative normally, then tack on the dr/dy
Okay. That _doesn't_ happen with 'r' terms though.
You take the derivative with r as normal. The derivative of r with respect to y only applies to the y variable
Thank you! That's what I needed to know.
Tell mertsj that I helped you. When you get the answer, let me know. I probably shouldn't have told you so early.
You do realize that finding dr/dy is only the first part. The second part is, you have to replace y = 5.75 to find r while keeping the volume constant
Honestly, I don't know how to tell him if he's not online, but if I see him chatting I will; I'm fairly new here. I will let you know when I get the answer. Thank you, and yes, I figured that part out. It was the implicit stuff that was killing me.
:D Okay, glad to help you.
And thank you for your time :)
Actually, we can go to a site called vyew
Then I can watch you do the steps
Uhh, is that...video chat? Because I think I'll pass for the afternoon, thanks.
I'm very close to the answer, just give me another minute or two.
It's not video chat. Why does everyone automatically assume video chat?
Might have to do with the 'watch' part.
It's just a site with an online whiteboard
Okay. I've got a tablet. My handwriting should be decent.
Yes, your handwriting was very nice. I figured you must have a tablet
Sorry, man. Let me keep working and see if I can figure out what I did wrong. I don't know why my microphone wouldn't work.
Well, I think it would be better if you worked on the mic, but okay
I can keep trying.
I got -1/5 this time. I'm checking wolframalpha.