Area of a Circle

Below, 2 congruent circles are shown. Press the START THE SHOW button and carefully watch the dynamics that take place.

Was the triangle formed truly a triangle? Explain why or why not.

What would we need to do to the number of peels in order to make this so-called triangle look more smooth (closer to a true triangle)?

What facet/part of the original circle is the base of this "triangle"?

What facet/part of the original circle is the height of this "triangle"?

Without Googling, write an expression that gives the area of circle in terms of its circumference and radius.

Suppose an above-the-ground circular swimming pool has a radius of 12 feet. What is the area of the exposed surface of the water it contains?

Suppose a circular track (that surrounds grass) has a circumference of 500 feet. If 3 bags of grass seed are needed to be spread out across every 100 square feet of grass in the circular region inside this track, determine how many entire bags of grass seed will be needed to cover the entire area of the circular region surrounded by this track.

Suppose a 12-inch pizza (pizza with diameter = 12 inches) costs $12.00. Suppose a 24-inch pizza costs $24.00. Which pizza is the better buy? Explain why this pizza is the better buy. (Assume both pizzas have the same thickness.)