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
2 answers
Question:
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
Answers
Assuming you mean that the circle touches the sides of the square, the area of the square would be 14 x 14 = 196 sq inThe area of the circle inside of the square is π (7)² = 153.9Therefore 196 - 153.9 = 42.1
Answer:Option [tex]42.1\ in^{2}[/tex]Step-by-step explanation:we know thatThe 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 circlesee the attached figure to better understand the problemStep 1Find the area of the squareRemember thatThe area of the square is [tex]A=b^{2}[/tex]whereb is the length side of the squarewe have[tex]b=14\ in[/tex]substitute[tex]A=14^{2}=196\ in^{2}[/tex]Step 2Find the area of the circleRemember thatThe 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 3Find the area of the region[tex]196\ in^{2}-153.9\ in^{2}=42.1\ in^{2}[/tex]
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