Question

A Wire of length 10 meter is cut into 2 portions ,One of them is bent to form a circle and the other is bent to form a square .
Find the radius of the circle and the side of the square when the sum of the areas of the circles and the square is minimum .

Answer 1

@satellite73 : May u check this ?

Answer 2

Do you have any ideas?

Answer 3

well,My attempt was :
1-I got the Area.
2-I differentiate dA/dx with respect to dA/dx =0
and then i stopped xD

Answer 4

alright what did you get the area function

Answer 5

Your restriction should be

\[x+y=10\]

Answer 6

Its not about the area function ,Its about the idea ..I dont even know if i started it right or not :/

Answer 7

but that's perimeter and you're looking for area so you need to relate the two

Answer 8

well you're minimizing

the area so you should be minimizing the area of a circle and an area of a rectangle

Answer 9

your restrictionis that you only have 10 meters of wire

Answer 10

That is the function you need ^ he related the perimeter and circumference to area. Now if you find the min area, you can solve for r

Answer 11

wait mertsj, isn't 10-2pir what is left after the circle meaning the parameter of the square is 10-2pir

Answer 12

perimeter*

Answer 13

A=A1+A2
\[\Large A=\frac{1}{16}X^{2} + \frac{1}{4\pi} (10-x)^{2}\]

Answer 14

if you have the radius as \(r\) then the area of the circle \(\pi r^2\) and the circumference is \(2\pi r\) so each side of the square is
\[\frac{10-2\pi r}{4}\] and its area is
\[\left(\frac{10-2\pi r}{4}\right)^2\]

Answer 15

total area is therefore
\[\pi r^2+\left(\frac{10-2\pi r}{4}\right)^2\] and that is what you are trying to maximize

Answer 16

minimize

Answer 17

He need the radius and the side ,When the circle and square are minimized .

Answer 18

OMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMG , I GOT IT !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! TY GUYS TY SOO MUCH !

Answer 19

The secret on the word 2 portions ,and When the circle and square are minimized .

Answer 20

oh minimized, sorry
but the same idea right?
and when you solve for \(r\) you still need to solve for the length that you use for the square, which should be easy enough since it is \(10-2\pi r\)

Answer 21

sattellite please help me

Answer 22

its about second derivative though ..

Answer 23

i cheated
minimum is at \(r=\frac{4}{5+\pi}\)
http://www.wolframalpha.com/input/?i= \pi+r^2%2B\left%28\frac{10-2\pi+r}{4}\right%29^2

Answer 24

the answer is 5/Pi+4 . Ty for your help :)