2.03: circumferences and areas of circles quiz

Which explanation can be used to derive the formula for the circumference of a circle?

First, find the relationship of the circumference to its diameter by finding that the length of the diameter wraps around the length of the circumference approximately π times. Use this relationship to writing an equation showing the ratio of circumference to diameter equaling π. Then rearrange the equation to solve for the circumference. Substitute the diameter for 2 times the radius.

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle. * Let s be the side length of the polygon, * let r be the hypotenuse of the right triangle, * let h be the height of the triangle, and * let n be the number of sides of the regular polygon. polygon area = n(12sh) Which statement is true?

As n increases, h approaches r so that rh approaches r².

What is the area of a circle with a diameter of 12.6 in.? Use 3.14 for pi and round your final answer to the nearest hundredth.

124.63

What is the area of a circle whose radius is 5 ft?

25π ft²

The circumference of a circle is 5π cm. What is the area of the circle?

6.25π cm²