Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. The diameter of the circle is 14 in.

Area of circle =πr²

Area of square = (side)²

Since the diameter = 14 ===> r = 7 ===> area circle =π.49 in²

area of square = 14x14=196 in²

area between square & circle = 196 - (3.1459) x 49 =42.1 in²

Answer Link

calculista calculista · Answer 2 · 2019-01-26T21:31:12+01:00

Answer:

Option [tex]42.1\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of the region that is inside the square and outside the circle is equal to the area of the square minus the area of the circle

see the attached figure to better understand the problem

Step 1

Find the area of the square

Remember that

The area of the square is

[tex]A=b^{2}[/tex]

where

b is the length side of the square

we have

[tex]b=14\ in[/tex]

substitute

[tex]A=14^{2}=196\ in^{2}[/tex]

Step 2

Find the area of the circle

Remember that

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=14/2=7\ in[/tex]

substitute

[tex]A=\pi(7^{2})=153.9\ in^{2}[/tex]

Step 3

Find the area of the region

[tex]196\ in^{2}-153.9\ in^{2}=42.1\ in^{2}[/tex]