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a cilindrical container of height h cm and radius r cm has both ends closed. It is produced using exactly 54pi cm2 of plastic.
i) express h in terms of r
ii) find the maximum possible volume of the container in terms of Pi.
I did the first part, i need the steps for part ii)!
You have the formula for the volume V in terms of h and of r. You've solved for h in terms of r.
Take the expression for h "in terms of r", and plug this in for "h" in the volume formula. This gives you the volume in terms only of r.
Differentiate, etc.
Hi, I`m new here but I think I can help(Hi)
The volume of the cylinder is given by the expression:
But, as you have h in terms of r, you can get:
Now, if you derivate the above expression and equal it to 0 you can get the answer I think, I`ll do it and post it here.
After a few calculations, I got a radius of 3, which leads us to a volume
I`m not sure, but, if anyone wants to check it out...