Question

A manufacturing company makes open cylindrical containers each with a capacity of 100cm^3. if the radius of the cylinders is r cm, find the value for which the area of the metal sheet required is minimum.

Answer 1

the capacity is 1000cm^3

Answer 2

typo

Answer 3

\(A = 2 \pi r h \)

\[ V = \pi r^2 h = 10^3 \]

substitute and then differentiate you will get your answer.

Answer 4

how do i get rid of h...

Answer 5

I gave you so many hints .. :)

Answer 6

ok so \(\large h=\frac{10^3}{\pi r^2} \) i substitute this and then differentiate...

Answer 7

Seems good to me.

Answer 8

when i substitute, i end up with \(\large A=\frac{2000}{r} \) ... how do i differentiate this and still get a value of r ?