Pi Problems

A circular pool has an area of 1962.5 square feet.  You are to construct a circular fence around the pool and exactly 10 feet from the edge of the pool.  How many feet of fencing do you need to buy.  (Use p » 3.14)

Three people whose heights are 6’4” , 5’6” and 5’2” decide to measure a giant tree.  They notice that when they all three wrap themselves tightly around the tree together (fingertips to fingertips) they can circle the tree entirely. Find the diameter of the tree.

Assume that everytime a dart is thrown at one of the dartboards that it hits the board and that it has an equal chance of hitting the board at any place. With those assumptions what is the probability that a dart will hit the small circle when a person throws a dart at the dart board? If the dart was thrown 100 times, how many would you expect to hit the bulls eye? What percentage would that be? Would it make a difference if the colored circle were moved on the dart board? Explain.

Board 1 Board 2

Find the area of each shaded region.  Which figure has the greatest shaded region?

Figure 1 Figure 2 Figure 3

A windshield wiper is 20 inches long from wiper motor.  The blade makes up the last 14 inches of the wiper.  It sweeps a path that has a central angle of 120 degrees.  Assuming that the wipers do not over lap, how much area does the pair cover when on?

When I order pizza I never know if I should order 2 medium or 1 large or if 3 medium is the same as 2 large or what. Then when there is a sale things really confuse me. How can I know? Maybe if you answer the questions: " Do 3 medium pizza really equal 2 large pizzas? and If not, which is more?" It would be enough information to help me know what to order.

The following chart may be helpful to organize information to answer the questions:

LARGE PIZZA                                               MEDIUM PIZZA
Diameter = ______                                    Diameter = ______
Total Area = ______                                  Total Area = ______

I have a friend that never eats the crust on a pizza and the other day we were discussing how much of the pizza is wasted for people that don't like crust? We thought that if we knew what percentage of the pizza was crust it would help us to know better how much was being wasted.

LARGE PIZZA                                               MEDIUM PIZZA

Diameter of toppings = ______              Diameter of toppings = ______
Radius of toppings = ______                   Radius of toppings = ______
Area of toppings = ______                       Area of toppings = ______
Area of crust = ______                             Area of crust = ______

What percent of the large pizza is crust?
What percentage is wasted?
What percent of the medium pizza is crust?
What percentage is wasted?
Is it better to waste crust on a medium pizza or large pizza?
Why?