Thursday

December 18, 2014

December 18, 2014

Posted by **lisa** on Saturday, March 2, 2013 at 10:17pm.

Find the height in centimeters of the most economical container.

- calculus -
**Reiny**, Saturday, March 2, 2013 at 11:57pmlet the radius be r

let the height be h

V = πr^2 h

πr^2 h = 20π

h = 20/r^2

Cost = .40(2πr^2) + .32(2πrh)

C = .8πr^2 + .64πr(20/r^2)

= .8πr^2 + 12.8π/r

dC/dr = 1.6πr - 12.8π/r^2

= 0 for a min of C

1.6πr = 12.8π/r^2

1.6r^3 = 12.8

r^3 = 8

r = 2

then h = 20/4 = 5

the cylinder should be 5 cm high and have a radius of 2 cm.

**Answer this Question**

**Related Questions**

business calculas - A cylindrical can is to hold 20 pie mraised to the 3rd power...

Calculus - A cylindrical drum is made to hold exactly 1m^3 in its interior. ...

Calculus - Optimization - A cylindrical container with a volume of 3000 cm^3 is ...

Math - A cylinder shaped can needs to be constructed to hold 400 cubic ...

Math (algebra) - Could you help me with this math question: A can in the shape ...

calculus - A rectangular box is to be constructed from two different materials. ...

Calculus - A cylindrical drum is made to hold exactly 1m^3 in its interior. ...

Calculus - The top and bottom of a can must be made of copper that costs two ...

Calculus - A rectangular box is to have a square base and a volume of 20 ft3. ...

calculus - A rectangular box is to have a square base and a volume of 50 ft3. ...