Posted by **:)** on Sunday, May 20, 2012 at 9:02pm.

A piece of wire 10 feet long is cut into two pieces. One piece is bent into the shape of a circle and the other into the shape of the square. How should the wire be cut so that the combined area of the two figures is as small as possible?

- Related rates -
**:)**, Sunday, May 20, 2012 at 9:03pm
i'm sorry, this is about optimization problems.

- Related rates -
**Damon**, Sunday, May 20, 2012 at 9:34pm
x and (10 - x)

x is 2 pi r

r = x/(2 pi)

Ac = pi r^2 = pi x^2/(4pi^2) = x^2/(4pi)

(10 -x) = 4*side = 4 s

so

s = (10-x)/4

As = s^2 = (100-20 x + x^2)/16

A= Ac+As = x^2/4pi + (1/16)(x^2-20x+100)

dA/dx = 0 for max or min

0= x/2pi +1/16 (2x-20)

0= .16 x + .125 x - 1.25

0= .285 x - 1.25

x = 4.4

- Related rates -
**Kassahun**, Wednesday, June 8, 2016 at 6:36am
5inches

## Answer This Question

## Related Questions

- Calculus - A piece of wire 12 m long is cut into two pieces. One piece is bent ...
- Math - A piece of wire 12 m long is cut into 2 pieces. One piece is bent into ...
- math - a piece of wire 12 meters long is cut into two pieces.one piece is bent ...
- Calc Optimization - A piece of wire 9 m long is cut into two pieces. one piece ...
- Math - A piece of wire 9 m long is cut into two pieces. One piece is bent into ...
- Math - You have a wire that is 35 cm long. You wish to cut it into two pieces. ...
- Math - A piece of wire of 14 meters long is cute into 2 pieces. One piece is ...
- differential calculus - a pc of wire 10feet long is cut into 2 pcs. one piece is...
- Pre Cal - a piece of wire 5 inches long is to be cut into two pieces. One piece ...
- Differential calculus - A piece of wire of length 2 m. is cut into two parts, ...

More Related Questions