Homework Help: Math

Posted by Kevin on Friday, March 15, 2013 at 5:18pm.

Optimization Problem

A right circular cylindrical can of volume 128tπ cm^3 is to be manufactured by a company to store their newest kind of soup. They want to minimize the surface area of the can to keep costs down.

What are the dimensions of the can with minimum surface area?

The volume of a cyllinder is V= πr^2h, where r is the radius and h is height. The surface area of a cylinder is SA= 2πr^2+2πrh, which is the sum of the area of the top and bottom (2 circles) and the area of the other curved sides (a rectangle, whose length is the circumference of the circles)

Math - Reiny, Friday, March 15, 2013 at 6:03pm
They have provided you with all the formulas you need
given: πr^2h = 128
h = 128/(πr^2)

so in
SA = 2πr^2+ 2πrh
= 2πr^2+ 2πr(128/(πr^2)
= 2πr^2 + 256/r
d(SA)/dr = 4πr - 256/r^2
= 0 for a min SA
4πr = 256/r^2
r^3 =64/π
r = 4/π^(1/3) = appr 2.7311
then h = 128/(πr^2) = 5.46223

notice that this is twice the radius
So the minimum SA is obtained when the
radius is 2.4311 cm
and the height is 5.46223 cm

Answer this Question

Related Questions

Geometry - Jake has two similar cylindrical pipes. The radius of the first ...
calculus - right circular cylindrical tin cans are to be manufactured to ...
geometry - A ball of diameter 20 cm fits exactly inside a cylindrical container...
geometry - Find the surface area of each of the following a cube that is 4 cm by...
maths --plse help me.. - A toy is in the shape of a right circular cylinder with...
Calculus - *Optimization problem* I'm okay at some optimization problems, ...
math - Find the approximate value of the volume of the right circular cone of 20...
Math - A right circular cylinder with a height of 20 cm and a right circular ...
math - the volume V of a right circular cone is V=(1/3)π r^2 h. If the ...
algebra am i right - Find the volume of a right circular cylinder whose base has...

For Further Reading

First Name:
School Subject:
Answer: