A circle contains a sector with an area of #75cm^2# and a central angle of #270°#. What is the radius of the circle to two decimal places?

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Answer 1 · 2018-07-31T17:47:20

# 5.64" cm(2dp)"#.

Let #r# be the radius of the circle.

The Area of a sector having central angle #theta" radian"# is #1/2r^2theta#.

WE have, #270^@=3pi/2" radian"#.

Hence, by what is given, #1/2r^2(3pi/2)=75#.

#:. r^2=(75xx4)/(3pi)=100/pi#.

#;. r=10/sqrtpi~~5.64" cm(2dp)"#.

Answer 2 · 2018-07-31T18:20:03

#r =5.64#cm

A sector is a fraction of a circle.
The fraction can be determined in three ways:

#("sector angle")/360" "or" "("arc length")/(2pi r)" "or" "("sector area")/(pir^2)#

In this case we are told that #3/4# of the area of the whole circle is #75cm^2#

#270/360 xx pi r^2 = 75#

#r^2 = (75 xx360)/(270 pi)#

#r^2 = 31.83#

#r =5.64#cm