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24) A wire 1 metre long is to be cut into two pieces. One piece is to be formed into a circle and the other into a square. Where should the cut be made in order that the sum of the areas of the circle and square be a minimum?

24) A wire 1 metre long is to be cut into two pieces. One piece is to be formed into a circle and the other into a square. Where should the cut be made in order that the sum of the areas of the circle and square be a minimum?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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24) A wire 1 metre long is to be cut into two pieces. One piece is to be formed into a circle and the other into a square. Where should the cut be made in order that the sum of the areas of the circle and square be a minimum?
Transcribed Image Text:24) A wire 1 metre long is to be cut into two pieces. One piece is to be formed into a circle and the other into a square. Where should the cut be made in order that the sum of the areas of the circle and square be a minimum?
Expert Solution
Step 1: Solution

It is given that the length of the wire is 1 metres and it is cut into two pieces.


Let the length of one piece is x metre and the other piece is (1-x) meter.

Since it is given that, one piece of wire is bent into the shape of a square, the length of the wire is equal to the perimeter of the square.

x = 4a

Or, a = x/4

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