Posted by **MM** on Thursday, December 6, 2012 at 8:28pm.

A solid is formed by adjoining one hemisphere to the top of a cylinder. The total volume of the solid is V (treat as a constant) cubic centimeters. Find the minimum surface area of the solid in terms of V.

- Calculus -
**Steve**, Thursday, December 6, 2012 at 10:28pm
with radius r and height h,

pi r^2 h + 2/3 pi r^3 = v

so,

h = 3(v - pi r^2)/(2pi r^3)

a = pi r^2 + 2pi r h + 2pi r^2

= 3pi r^2 + 2pi r h

= 3pi r^2 + 3(v - pi r^2)/r^2

= 3pi r^2 - 3pi + 3v/r^2

da/dr = 6pi r - 6v/r^3

dv/dr = 0 when r^4 = v/pi

a(∜(v/pi)) = 3pi√(v/pi) - 3pi + 3√(pi*v)

= 3√pi (2√v - 1)

as usual, double-check the arithmetic and the algebra. I'm pretty sure about the calculus.

- Calculus -
**MM**, Friday, December 7, 2012 at 9:38am
thanks a ton.

## Answer This Question

## Related Questions

- Calculus - A solid is formed by adjoining two hemispheres to the ends of a right...
- Mathematics - Given solid object is made up of a hemisphere snd a cyinder.the ...
- Calculus - A solid is formed by adjoining two hemispheres to the ends of a ...
- Calculus - A solid is formed by adjoining two hemispheres to the ends of a ...
- math - matt used centimeter cubes to make a solid that had a volume of 5 cubic ...
- math stumped... - is the solution of 1/3x=21? greater than or less than 21? the ...
- calculus - 1. A solid is constructed so that it has a circular base of radius r ...
- calc - the volume of a cylindrical tin can with a top and a bottom is to be 16*...
- Math - A metal solid cylinder of radius 6 cm and length 12 cm is ,melted and ...
- math - a figure on the left is the base of a right solid whose sides are 10 ...

More Related Questions