Yes. That's exactly what it is. Good work !
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No. The diagonal of the rectangle is a little over 32.2, and nothing that long can fit into a circle with a diameter of 27.
Infinity because the circumference of the circle is the same as the circumference of the sphere.
Yes because the diameter of the circle is less than the sides of the square.
4 because there are 360 degrees around a circle
It depends on the diameter of the circle and the width of the square, if they are the same then the answer is no. If you draw yourself a square then inscribe a circle with a radius of half the length of a side of the square, the circle will fit inside the square but the corners of the square will be outside the circle. Thus by inspection the area of the square is larger than the area of the circle.