A solider is parachute training. He jumps out of a plane high enough that the pilot determines the solider will land somewhere in an 240 foot radius land zone. The pilow forgot to mention to the solider that the parachute has very little maneuverablity (no steering). and there are 30 trees in the landing zone. Each tree from the air practically outlines a circle with a radius of 8 feet. What is the geometric probability that the solider will land in a tree?

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Mathematics

16 August, 19:59

A solider is parachute training. He jumps out of a plane high enough that the pilot determines the solider will land somewhere in an 240 foot radius land zone. The pilow forgot to mention to the solider that the parachute has very little maneuverablity (no steering). and there are 30 trees in the landing zone. Each tree from the air practically outlines a circle with a radius of 8 feet. What is the geometric probability that the solider will land in a tree?

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Dakota Wu · Answer 1

1/30

Step-by-step explanation:

The area of the landing zone is ...

A = πr² = π·240²

landing zone area = π (30²) (8²)

The area of a tree is ...

A = πr² = π·8²

so the area of 30 trees is ...

total tree area = 30 (π·8²)

and the probability of landing in a tree is the ratio of areas:

p (landing in tree) = (total tree area) / (landing zone area)

= (π·30·8²) / (π·30²·8²) = 1/30