In a circle, a 90° sector has area #16pi# #ft^2#. What is the radius of the circle?

1 Answer
Alan P.
Apr 10, 2018

Radius: #8# feet

Explanation:

If a #90^circ# sector (i.e. a quarter) of a circle has an area of #16pi" ft"^2#
the the entire circle has an area of #4xx16pi" ft"^2=64pi" ft"^2#

Since #"Area"_circ=pir^2#
if #"Area"_circ=64pi" ft"^2#
then #pir^2=pi64" ft"^2#
#rarr color(white)("xx")r^2=64" ft"^2#
#rarr color(white)("xx")r=8" ft"#

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