Week 28 CAPT Problem - 10th Grade


Circles


The table below shows that the value C, the circumference of a circle, is dependent on d, its diameter.

d units C units
1 3.14
2 6.28
3 9.42
4 12.56
.
.
.
 		.
.
.
10 31.4

An equation that shows the relationship between the diameter of the circle and its circumference is C = Πd where 3.14 is used for Π.

  1. What is the diameter of the circle with a circumference of 26.69 units?

  2. Draw a line graph that shows the relationship between the diameter of a circle and its circumference. Be sure to label the both axis.

  3. Explain how you could use your graph to approximate the circumference of a circle with a diameter of 8 units.

  4. What percentage of the area of a square with side 6 is the area of a circle with a diameter of 6?

    What percentage of the perimeter of a square with a side of 8 is the circumference of a circle with a diameter of 8?

    Based on the above answers, what generalization can you make about the relationship between a circle and the square that surrounds it?