Sunday

March 1, 2015

March 1, 2015

Posted by **JEZRELL** on Saturday, February 23, 2013 at 11:43pm.

- Elementary Analysis -
**Steve**, Sunday, February 24, 2013 at 6:47amYou know that

pi r^2 h = 1000, so

h = 1000/(pi r^2)

the surface area is

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

= 2pi r^2 + 2pi r * 1000/(pi r^2)

= 2pi r^2 + 2000/r

da/dr = 4pi r - 2000/r^2

= (4pi r^3 - 2000)/r^2

Since r > 0, da/dr=0 when

4pi r^3 = 2000

r^3 = 2000/4pi = 500/pi

r = 5 ∛(4/pi) ~= 5.42

go to wolframalpha.com and enter

plot y = 2pi r^2 + 2000/r where 3<r<8

to see where it is minimum

**Answer this Question**

**Related Questions**

calculus - a. A closed cylindrical can is to hold 1000cm^3 of liquid. How should...

math - you are designing a 1000-cm^3 right circular cylindrical can whose ...

Calculus1 - You are designing a 1000 cubic cm closed cylindrical can with radius...

Math - An aluminum cylindrical juice can has a height of 4 in. and a radius of 6...

math - An aluminum cylindrical juice can has a height of 4 in. and a radius of 6...

Pre-Calc - Starkist tuna company will package tuna fish in 2-L cans. Find the ...

math - the volume of an cylindrical can with a radius r cm and height h cm is ...

geometry - A cylindrical tin can holding 2 gal.has its height equal to the ...

solid mensuration - A cylindrical tin can holding 2 gal.has its height equal to ...

math - find the radius and height of a cylindrical soda can with a volume of ...