A circle contains a sector with an area of 75cm^275cm2 and a central angle of 270°. What is the radius of the circle to two decimal places?

2 Answers
Jul 31, 2018

5.64" cm(2dp)".

Explanation:

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)".

Jul 31, 2018

r =5.64cm

Explanation:

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 =5.64cm