A company that organizes graduation events makes diplomas tubes from square sheets of paper. In order for all diploma tubes to be identical, each leaf is wrapped very tightly around a wooden cylinder of diameter d (centimeters), going 5 complete turns around that cylinder. At the end, a cord is tied in the middle of the diploma, tightly, so that unwinding does not occur, as illustrated in the figure. Then, the wooden cylinder is removed from the middle of the rolled paper, completing the making of the diploma. Consider that the thickness of the original sheet of paper is minimal. What is the measure, in centimeters, of the side of the sheet of paper used in making the diploma?

a) Point A is the center.

b) Point C is the center.

c) Point H is the center and is tangent to the circumference.

a) Point O is the center.

b) Point O is the center.

4 (Dolce & Pompeu-adapted) Determine the perimeter and area of the shaded figure. Note that the area is formed by 10 m arcs that are centered on A, B and C.

5- Calculate the length of a circle and the area of the circle whose radius measures 4 cm.

6 (Dolce & Pompeu) The length of a circle is cm. Determine the radius of another circle whose length is four times smaller than the length of the first circle.

7 (Dolce & Pompeu) A circular track was built by two concentric circles, whose lengths are approximately 1500 m and 1200 m. What is the length of this track?

a) Point A is the center.

a) Point A is the center.

9- Determine the area of the circular segment: