The circumference of a circle is $11pi$ inches. What is the area, in square inches, of the circle?

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Answer 1 · 2017-03-29T17:04:58

$~~95 "sq in"$

We can derive the diameter of the circle by:
$"Circumference"=pi*"Diameter"$
$"Diameter"="Circumference"/pi=(11pi)/pi=11 "inches"$

Hence, the area of the circle:
$"Area of circle"=pi*("Diameter"/2)^2=pi*(11/2)^2~~95 "sq in"$

Answer 2 · 2017-03-29T17:07:54

The circumference of a circle having radius $r$ is $2pir.$

Hence, by what is given, $2pir=11pi rArr r=11/2.$

$":. The Area of the circle="pir^2=pi(11/2)^2=30.25pi" sq. in."$

Answer 3 · 2017-03-29T17:47:35

$color(red)(95$ inches² to nearest inch²

circumference of a circle $=2pir$

circumference given $=11pi$

$:.2pir=11pi$

divide L.HS.and R.H.S. by $pi$

$:.2r=11$

$:.r=11/2$

$:.r=5.5$

Area of the circle $=pir^2=pi*(5.5)^2$

$:.=3.141592654*(5.5)^2$

$:.color(red)(=95$ inches². to the nearest inch²

The circumference of a circle is 11pi11pi inches. What is the area, in square inches, of the circle?