external surface area of a closed cylinder
=
external surface area for one open end of cylinder
=
=
obtain an expression for h.
volume of cylinder
=
substitute the value of h into the volume equation
Question:
A hollow circular cylinder, open at one end, is constructed of thin sheet metal. The total external surface area of the cylinder is . The cylinder has a radius of and a height of .
(i) Express h in terms of r and show that the volume, , of the cylinder is given by:
Given that can vary,
(ii) Find the value of for which has a stationary value,
(iii) find this stationary value and determine whether it is a maximum or a minimum.
(i) Can someone please show me how to get ?
Definition:A point 'u' at which the derivative of a function f(x) vanishes,i.e. f'(u) = 0 is called a stationary point.
This means you have to find values of r such that V'(r) = 0.
yup just like what isomorphism said, a stationary point can be found when the derivative of V with respect to r is 0
earlier you already prove the equation of the volume:
hence all you need to do is to differentiate this equation with respect to r and equate it to 0:
solve for r. good luck