The volume of a right circular cylinder tin is V=pi.r^2h and the surface area of the cylinder is A=2pi.r^2+2pi.rh, where r is the radius of the end faces and h the height.
(i) Show that A=2pi.r^2+2V/r
(ii) With V kept constant find dA/dr
(iii) Show that h=2r gives a minimum for A for a constant V
(iv) Find the radius and height of the tin which has a minimum area of the metal for a volume of 269.5 cm^3.

Question

The volume of a right circular cylinder tin is V=pi.r^2h and the surface area of the cylinder is A=2pi.r^2+2pi.rh, where r is the radius of the end faces and h the height.
(i) Show that A=2pi.r^2+2V/r
(ii) With V kept constant find dA/dr
(iii) Show that h=2r gives a minimum for A for a   constant V
(iv) Find the radius and height of the tin which has a minimum area of the metal for a volume of 269.5 cm^3.

anonymous · Answer

A cylinder has a diameter of 80 cm and a length of 45 cm. Another cylinder has the same volum

hero · Answer

Numbers, that is a Calculus problem