Question

A point is chosen at random in the circle. What percent of the time will the point be in the square? Round to the nearest tenth of a percent.

Answer 1

`63.7\%`

Explanation:

we know that

To find the percent divide the area of the square by the area of the circle

step 1

Find the area of the circle

The area of the circle is

`A=\pi r^(2)`

we have

`r=1\ in`

substitute the values

`A=(3.14)(1)^(2)=3.14\ in^(2)`

step 2

Find the area of the square

The area of the square is

`A=b^(2)`

where

b is the length side of the square

we have

`D=2\ in` ---> the diagonal of the square is equal to the diameter of the circle

Applying Pythagoras Theorem

`D^(2)=b^(2)+b^(2)`

substitute the values

`2^(2)=2b^(2)`

`4=2b^(2)`

`b^(2)=2\ in^(2)` ------> the area of the square

step 3

Find the percent

`(2)/(3.14)= 0.6369`

Convert to percent

`0.6369*100=63.69\%`

Round to the nearest tenth of a percent

`63.7\%`