Question

A sector of area 21 square miles is formed by a central angle of 3.1 radians. Find the radius of the circle?

Answer 1

The radius of the circle is 3.68 miles.

Explanation:

Area of a full circle : `A=pi*r^2`

A circle is 360 deg, that is 2 radians ( 180 deg is 1 radian)

So Area of a sector in terms of radians is:`1/2r^2theta` where `theta` is angle at center in radians

Solve this: `21=1/2r^2 * 3.1`
`r^2=21*2/3.1`

So `r=3.68` miles

Answer 2

`"radius "=3.68" miles"`

Explanation:

`• " area of sector "="area of circle "xx"fraction of circle"`

`rArrcancel(pi)r^2xx3.1/(2cancel(pi))=21`

`rArr3.1r^2=42`

`rArrr=sqrt(42/3.1)~~3.68" miles"`