SOLUTION: A leaf falls from a tree into a yard, 1000 cm * 600 cm. Two round buckets are in the yard. One bucket has a 25 cm diameter, while the other bucket has a 50 cm diameter. What is the

Algebra ->  Probability-and-statistics -> SOLUTION: A leaf falls from a tree into a yard, 1000 cm * 600 cm. Two round buckets are in the yard. One bucket has a 25 cm diameter, while the other bucket has a 50 cm diameter. What is the      Log On


   

Question 1140696: A leaf falls from a tree into a yard, 1000 cm * 600 cm. Two round buckets are in the yard. One bucket has a 25 cm diameter, while the other bucket has a 50 cm diameter. What is the probability of the leaf landing in one of the buckets?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the total area that the leaf can fall into.
Find the total area of the buckets that the leaf can fall into.
The probability will be the ratio of the two areas.
A%5Btot%5D=1000%2A600
A%5Btot%5D=600000
The area of each bucket would be,
A=%28pi%2F4%29%28D%5E2%29
So,
A%5B1%5D=%28pi%2F4%29%2825%5E2%29=%28625%2F4%29pi
A%5B2%5D=%28pi%2F4%29%2850%5E2%29=%282500%2F4%29pi
Adding them,
A%5Bb%5D=%28625%2F4%29pi%2B%282500%2F4%29pi
A%5Bb%5D=%283125%2F4%29pi
So,
P=%28%283125%2F4%29pi%29%2F600000
P=pi%2F768