Either you are thinking too much or you are commiting a mistake in solving equation.
...now you will not get r=0 on differentiating.
Infavt, if you use for determining maximum volume, steps will be easier.
A circular cylinder is inscribed in a fixed sphere with radius 18cm such that all the points on the circ of both cylindrical ends are always lying on the spherical surface. Given that the cylinder has a ht of h cm and cylindrical base radius of r cm, show that (done)
Initially the ht of the cylinder is 24cm and is decreasing at constant rate of 0.25cm/s
(ii) show that rate at which radius is changing at this instant is cm/s (done)
(iii) Find the time taken for the volume of the cylinder to reach its maximum value. (you need not verify that the volume is maximum) Ans:12.9s
ok part (iii) is the one i need help in. highlight beside it for ans.
i know that max value for volume means but then i'll just get r=0 when i sub in h=24.
then if i use the h and r eqn, i just get r=0 again.
in truth i'm clueless how to continue... is max volume just taking the given values of h and r, then using that divide by ? if so then i couldn't find that either :/ maybe i'm just thinking too much x.x
You are told that the initial height of the cylinder was 24 cm and you know, from (a), that [tex]h^2+ 4r^2= 1296[tex] so the initial radius is given by . [tex]4r^2= 1296- 576= 720[tex]. , and . Subtract that from your value of r that gives a maximum volume. Since you know that r "is decreasing at constant rate of 0.25cm/s" dividing that difference by .25 gives the time in seconds.
(I would be inclined to leave the value of r that gives maximum volume in terms of radicals rather than as "a strange decimal".)