Question

A dog is leashed to the corner of a house with a 14 foot leash. How much running area does the dog have? Round your answer to the nearest square footThe dog has aboutsquare feet of running area.

Answer 1

Step-by-step explanation

Without the house the running area would form a circle with a 14 ft radius. Since the corners of the house describe a 90° angle then the house covers a quarter of the entire circle. Therefore the running area will be three quarters of the area of a 14 ft radius circle. The area if a circle with radius r is given by:

`A=\pi r^2`

Then 3 quarters of the area of a 14 ft radius circle are given by:

`(3)/(4)\cdot A=(3)/(4)\cdot\pi\cdot(14ft)^2=461.81ft^2`Answer

We must round the answer to the nearest square foot. Then the answer is:

The dog has about 462 square feet of running area.