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

Question

23264 views around the world

You can reuse this answer
Creative Commons License

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