A vacuum flask (for keeping drinks hot) is modelled as a closed cylinder in which the internal radius is r cm and the internal height is h cm.
The volume of the flask is 1000 cm³. A flask is most efficient when the total internal surface area, A cm², is a minimum.
(i) Show that A = 2π2²+ 2000/2
(ii) Given that r can vary, find the value of r, correct to 1 decimal place, for which A has a stationary value and verify that the flask is most efficient when r takes this value.
