Wednesday

July 30, 2014

July 30, 2014

Posted by **saud** on Monday, November 21, 2011 at 12:40am.

- calculus -
**Anonymous**, Monday, November 21, 2011 at 1:26amV = r ^ 2 ð h

64 ð = r ^ 2 ð h Divide both sides with ð

64 = r ^ 2 h Divide both sides with r ^ 2

64 / r ^ 2 = h

h = 64 / r ^ 2

A = 2 r ^ 2 ð + 2 r ð h

A = 2 r ^ 2 ð + 2 r ð 64 / r ^ 2

A = 2 r ^ 2 ð + 128 r ð / r ^ 2

A = 2 r ^ 2 ð + 128 ð / r

d A / d r = ( 4 ð ( r ^ 3 - 32 ) ) / r ^ 2

Function has extreme value where first derivative = 0

dA / dr = 0

Solutions:

r = -1.5874 + 2.7495 i

r = -1.5874 2.7495 i

and

r = 2 2 ^( 2 / 3 ) = 3,1748

So :

r = 2 2 ^( 2 / 3 ) = 3,1748

Second derivative :

4 ð ( 64 / r ^ 3 + 1 ) =

4 ð ( 64 / 32 + 1 ) =

4 ð ( 2 + 1 ) =

4 ð 3 = 12 ð > 0

Remark : r ^ 3 = [ 2 2 ^( 2 / 3 ) ] ^ 3 = 32

If second derivative > 0

that is minimum value of function.

So :

r = 2 64 / [ 2 2 ^( 2 / 3 ) ] ^ 2

h = 64 / r ^ 2

h = h = 64 / [ 2 2 ^( 2 / 3 ) ] ^ 2

h = 4 2 ^( 2 / 3 )

- calculus -
**Anonymous**, Monday, November 21, 2011 at 1:54amð = pi number

**Related Questions**

Math - How to setup this equation? Find the ratio of the surface area of a ...

Calculus - an open topped cylinder has a volume of 125 cubic inches. determine ...

geometry - find the surface area of the figure below. A cylinder which has a ...

Algebra 1--How Am I Supposed to Solve This?! - Suppose a cone and a cylinder ...

calculus - 1. The radius of a sphere is r inches at time t seconds. Find the ...

calculus - The radius of the base of a right circular cylinder is r com and the ...

Calculus - A right circular cylinder is inscribed in a cone with height h and ...

Calculus - Find the radius, volume, and hieght of the right- circlar cylindar ...

calculus - A potter forms a piece of clay into a cylinder. As he rolls it, the ...

Math - the formula for the surface area of a cylinder is: A=2πrh+2πr^2...