You have a wire that is 77 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

Question

3 years ago

6

You have a wire that is 77 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

ther piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum?

Mathematics

1 answer:

Serga [27] · Answer 1 · 2022-08-29T17:53:20+03:00

Answer:

23.62 cm

Step-by-step explanation:

The question asking for a condition when the total area of the square and the circle(A) is minimum/lowest. To find the lowest area you can get, you have to differentiate the formula for the total area(A).

The wire is 77cm long, let's say x is the square side and r is the circle radius. Then it will be

77cm= 4x + 2 * π * r

4x= 77cm - 2 * π * r

x= (77cm - (π * r ))/4

Square area is x^2 while circle area is π *r^2. Total area will be:

A= square area + circle area

A== x^2 + π *r^2

A= ( (77 - (π r ))/4 ) ^2 + π *r^2

A=(5929- (144 * π r ) + π^2 r^2)/ 16 + π *r^2

A= 370.56 - 9 π r + π^2 r^2/16 + π *r^2

A= 370.56 - 28.26 r + 0.616r^2 + 3.14*r^2 =

A= 370.56 - 28.26 r + 3.756 r^2