Finding Height and Radius using derivatives

[mrderson]

A cylinder is inscribed in a right circular cone of height 7 and
radius (at the base) equal to 3.5. What are the dimensions of such a
cylinder which has maximum volume?

Radius =
Height =

I am on spring break so i can't ask my teacher to explain this problem
to me, and i am not sure how to finish the problem.


I thought that you would start with
7/3.5=x/r
then
3.5x=7r
then
x=2r
then i thought you would put the 2r into
H=7-x
so
H=7-2r
then i put pir^2 in front of it so it is
pir^2(7-2r)
Then i thought you would find the derivative to find r then plug it
into H=7-2r to find the height. but i didn't know how to find the
derivative with pi so i got stuck.

 

[wjm11]

A cylinder is inscribed in a right circular cone of height 7 and
radius (at the base) equal to 3.5. What are the dimensions of such a
cylinder which has maximum volume?

H=7-2r
then i put pir^2 in front of it so it is
pir^2(7-2r)
Then i thought you would find the derivative to find r then plug it
into H=7-2r to find the height. but i didn't know how to find the
derivative with pi so i got stuck.

You’re doing great. Just multiply out/distribute

pir^2(7-2r) = 7(pi)r^2 – 2(pi)r^3

Now just use the Power Rule to find the derivative. (Remember, pi is just another constant – not a function of x. Don’t be confused by that.)

Set the derivative equal to zero and solve for r.