A thin rope 200 inches length is going to be cut into three pieces to form one circle and two equal squares. Which of the following represents the #r# of the circle, if the rope was finally cut in such a way that the total area of the shapes is minimized?
1 Answer
Explanation:
Rope is 200 inches long.
Let Length of Rope
Now Rope is going to be cut into three pieces to form one circle and two equal squares.
Let radius of circle
Side of Square
Perimeter of Circle
perimeter of Square
Note- Both squares are same.
in the question it mentioned that the total area of shapes are minimum.
We are going to use Differentiation method to Find extreme point and then find maxima and minima at all extreme points.
Put value of
Differentiate with respect to r
For Extreme points
we know that
Hence
Multiply equation with 4
Now we have to check whether value of r gives us maximum area or minimum area.
Now again differentiate the (equation 1) with respect to r.
We have only one value of
Hence