# Calculus!!!

A piece of wire 28 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
(a) How much wire should be used for the square in order to maximize the total area? (b) How much wire should be used for the square in order to minimize the total area?

1. 👍
2. 👎
3. 👁
1. a) that part is trivial, the largest area is obtained if all of the wire is used to make a circle

b) let the radius of the circle be r
let the side of the square be x

4x + 2πr = 28
2x + πr = 14
x = (14-πr)/2

A = x^2 + πr^2
= (14-πr)^2 /4 + πr^2

dA/dr = (1/2)(14-πr)(-π) + 2πr = 0 for a max/min
simplifying ...
4r = 14 - πr
4r + πr = 14
r = 14/(4+π)

we need 2πr to form the circle, so the wire should be cut at
2π(14/(4+π)) or appr 12.32 m

check my arithmetic

1. 👍
2. 👎
2. 14/(pi +4)

1. 👍
2. 👎

## Similar Questions

1. ### Calculus

A piece of wire 40cm long is cut into two pieces. One piece is bent into the shape of a square and the other is bent into the shape of a circle. How should the wire be cut so that the total area enclosed is a) a maximum? /b) a

2. ### maths

a 10m piece of wire is cut into two pieces one piece is 2m longer than the other. how long are the pieces?

3. ### Calculus Help Please Urgent!!!

A piece of wire 14 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? 14 m this

4. ### Related rates

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

1. ### Pre-Calc

A piece of wire 100 cm long is cut into two pieces. One piece is bent to form a square and the other to form a circle. Let x equal the length of the wire used to form the square. A. write the function that represents the area of

A piece of wire 168cm. long is to be cut into two pieces, each to be bent to make a square. The lenght of a side of one square is to be 2cm. greater than the lenght of aside of the other. What is the area of the smaller square?

3. ### algebra

A 28​-inch board is to be cut into three pieces so that the second piece is twicetwice as long as the first piece and the third piece is 44 times as long as the first piece. If x represents the length of the first​ piece, find

4. ### HELLP!! calculus

A piece of wire 25 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much of the wire should go to the square to maximize the total area enclosed by both figures? (b) how

1. ### Calculus

a piece of wire 12 ft. long is cut into two pieces. one piece is made into a circle and the other piece is made into a square. Let the piece of length x be formed into a circle. allow x to equal 0 or 12, so all the wire is used

2. ### Math

A 14 inch board is to be cut into 3 pieces so that the second piece is twice as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece find the lengths of

3. ### geometry

A wire 10 meters ong is to be cut into two pieces. One piece wil be shaped as a square, and the other piece will be shaped as a circle. (piece one is 4x, piece two is 10-4x) a)Express the total area A enclosed by the pieces of

4. ### Math

A wire 32 cm long is cut into two pieces. The longer piece is 6 cm longer than the shorter piece. What is the length of the shorter piece?