Posted by Ashley on Wednesday, November 7, 2012 at 3:13pm.
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 2 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to three decimal places.)

Calculus  Steve, Wednesday, November 7, 2012 at 3:24pm
if the cylinder is of radius r and height h, the volume v is
v = 4/3 pi r^3 + pi r^2 h
so, h = (v  4/3 pi r^3)/(pi r^2)
h = (2  4/3 pi r^3)/(pi r^2)
the surface area a is
a = 4pi r^2 + 2pi r h
= 4pi r^2 + 2pi r (2  4/3 pi r^3)/(pi r^2)
= 4pi r^2 + 2/r (2  4/3 pi r^3)
= 4pi r^2 + 4/r  8pi/3 r^2
= (4pi  8pi/3) r^2 + 4/r
= 4pi/3 r^2 + 4/r
maximum area where da/dr = 0
da/dr = 8pi/3 r  4/r^2
= (8pi/3 r^3  4)/r^2
da/dr=0 when r = ∛(3/2π)
As usual, check my math to verify result.

Calculus  Ashley, Wednesday, November 7, 2012 at 3:30pm
Is pi in the denominator?

Calculus  Steve, Wednesday, November 7, 2012 at 3:39pm
yes.

Calculus  a, Tuesday, October 25, 2016 at 8:53pm
what is r?
Answer This Question
Related Questions
 Calculus  A solid is formed by adjoining one hemisphere to the top of a ...
 Calculus  A solid is formed by adjoining two hemispheres to the ends of a right...
 Calculus  A solid is formed by adjoining two hemispheres to the ends of a right...
 Math (calculus) (optimization)  A solid is formed by adjoining two hemispheres ...
 Math  A metal solid cylinder of radius 6 cm and length 12 cm is ,melted and ...
 Math  Geometry  A cylindrical solid has a cylindrical circular hold drilled ...
 Calculus  Find the radius, volume, and hieght of the right circlar cylindar ...
 calculus  This one is tough. "A ballon in the shape of a cylinder with ...
 math  A right cylinder has a total surface area of 471 square centimeters. The ...
 Geometry  If the edges of a rectangular prism are 8cm, 6cm, and the diagonal is...
More Related Questions