After a one-piece circular tablecloth of maximum possible area was cut

To maximize the area of the circle, diameter of the cloth = d = min(a,b) , where a and b are the sides of the rectangular piece

Area of remaining portion = \(a*b - \frac{\pi*d^2}{4 }\)

Statement 1=

We know a and b; hence we can find d.

Sufficient

Statement 2-

We know d; hence we can find the shorter side of the rectangle. We have no idea about the longer side.

Insufficient

I'm sorry, but the solution is still not clear to me. How is the answer A and not C?

We only know that the figure is a rectangle.
We don’t know whether the rectangle is a square or not.

The circle we can draw within a rectangle will be limited by the shorter side (here the circle must stay within the boundaries of the rectangle)

Imagine a circle with diameter 4.

The MAX Area circle we could draw would be perfectly inscribed within a square with equal side lengths of 4.

Now imagine the square is stretched along its length.

We now have a rectangle with width = 4 and the length = 100

Again, the MAX circle we can draw within this rectangle will have a diameter of 4: the same circle as in the case of the square with side length 4.

The circle is a set of equidistant points from the center. Hence, no matter how we tried to draw the circle, we are limited by the shorter side of the rectangle.

Hope that helps a bit? 🙂

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