Approximating pi with darts

Objectives: 1. Provide the student with an understanding of the relationship between the probability of randomly selecting a point on the board and the ratio of the area of the circle to the area of the square.

2. Allow the student to explore how they could extend the same idea to three dimensions using volumes of a cube and volumes of a sphere.

1. To approximate pi we used an approximation for the probability that a dart will hit the circle. What is the true probability that the dart will hit he circle?

2.What happens to the approximation of pi as the number of darts gets very large?

2. By copy and pasting the address below into the address bar you can see a .gif image that shows a 3D approximation of pi using a sphere inscribed in a cube. Following the steps used in the applet. find the expression for estimating pi using the volume of a square, volume of a cube and randomly selecting points within the figure.
http://5010.mathed.usu.edu/Fall2013/PClayton/Pi with sphere.gif

Paul Clayton, 9 November 2013, Created with GeoGebra