# Math Help - Geometric Word Problem

1. ## Geometric Word Problem

Trisha ties her dog to a stake in her backyard by using either a chain or leash, as shown below. The chain allows the dog unobstructed movement for up to 20 feet from the stake in all directions. The leash allows the dog unobstructed movement for up to 15 feet fromt he stake in all directions. The dog's area of movement allowed by the chain is about how many square feet more than the area of movement allowed by the leash?

How is the solution 550?

2. Originally Posted by donnagirl
Trisha ties her dog to a stake in her backyard by using either a chain or leash, as shown below. The chain allows the dog unobstructed movement for up to 20 feet from the stake in all directions. The leash allows the dog unobstructed movement for up to 15 feet fromt he stake in all directions. The dog's area of movement allowed by the chain is about how many square feet more than the area of movement allowed by the leash?

How is the solution 550?
Area of a Circle = $(\pi)(r^2)$

So subtract the larger circular area (the chain area) from the smaller circular area (the leash area):

$\pi(r_1)^2$ - $\pi(r_2)^2$ where $r_1=20$ and $r_2=15$

This will yield how much more area the chain allows the dog than the leash. I'm assuming they rounded the answer to the nearest foot?