Question
Asked Nov 5, 2019

A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and square. What should the wire be cut to (a) maximize and (b) minimize the combined area of the circle and the square?

check_circleExpert Solution
Step 1

Let x be the length of the wire cut for the circle then the length of the wire cut for the square.

If x be the length of the wire cut for the circle then the circumference of the circle is x.

2r x
х
2л
Obtain the area of the circle.
2.
х
= T
2л
47T
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2r x х 2л Obtain the area of the circle. 2. х = T 2л 47T

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Step 2

Let 60 – x be the length of the wire cut for the square then the perimeter of the square is 60 – x.

4s 60 x
60- х
4
Obtain the area of the square.
60- х
4
60
4
4
3600 2
60x
16
16
8
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4s 60 x 60- х 4 Obtain the area of the square. 60- х 4 60 4 4 3600 2 60x 16 16 8

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Step 3
The total area of the circle and square is A(x)= nr
3600
60x
A(x)
4л
16
16
3600 x
60x
with respect to x and equate the
Differentiate A(x)=
4л
16
16
derivative to zero to find the critical point.
2х 60
0+
47
2x
A'(x)
16
8
60
X
27
help_outline

Image Transcriptionclose

The total area of the circle and square is A(x)= nr 3600 60x A(x) 4л 16 16 3600 x 60x with respect to x and equate the Differentiate A(x)= 4л 16 16 derivative to zero to find the critical point. 2х 60 0+ 47 2x A'(x) 16 8 60 X 27

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