For d) substitute the x-value you found gives the maximum into the equationHi, I'm a bit stuck on a couple of things.
A cylindrical biscuit tin has a close-fitting lid which overlaps the tin by 1 cm. The radii of the tin and the lid are both x cm. The tin and the lid are made from a thin sheet of metal of area 80pi cm^2 and there is no wastage. The volume of the tin is V cm ^3.
a) is show that V = pi(40x-x^2-x^3)
which I've done.
b) use differentiation to find the positive value for which V is stationary. I've got this to be 10/3, which I think is right.
c) Prove that this gives a maximum value of V.
I've done this ok, too.
d) Find this maxium value of V. I'm probably being really stupid, but this is the bit I can't do. I've tried a couple of things but I'm not coming out with the right answer.
e) The last bit is 'determine the percentage of the sheet metal used in the lid when V is a maximum'. Also not sure where to start with this. Can anyone give me any pointers?