The circumference of a circle is 10pi. Which of the following is not

Radius of the circle=5. Therefore Area is 25pi = 78.5
E) 40 root 2 > 78.5

Think about it - what is the constraint on a rectangle inside a fixed circle?

It can have very very little area (say the blue rectangle). Then we can start expanding it till it becomes the yellow rectangle (which is actually a square). If we try to expand it any more, its area will start decreasing again till it becomes very very small again (the green rectangle).



Hence, there is no minimum area of the rectangle but there is a maximum possible area dependent on the value of the radius. So if 40 is an acceptable area of a rectangle, then 30 is certainly acceptable too. If 30*sqrt(2) is acceptable (which is about 42), then 40, 30 and 20*sqrt(2) are certainly acceptable too. Hence, the only value that would not be acceptable is the greatest value given i.e. 40*sqrt(2).

Answer (E)

R = 5, when diagonal is drawn in a rectangle it passes through the centre of the circle circumscribing it. The diagonal divides the rectangle into a 45-45-90 right triangle.The side opposite 90 is the length of the diagonal,so 10=root2X, so x=5root2. This makes the length and breadth of the rectangle the same, area = (5root2)^2=50 this is the maximum area as the area of rectangle is at its maximum when it’s a square,
Option e says area could be 40root2 = which is slight greater than 50(root2=1.4)