Question

The area of the sector formed by the 110 degree central angle is 50 units squared. What is the radius of this circle??

Answer 1

Hello,
Let make a rule of three.

For 360° area of the circle is π R²
For 1° ............of the sector .. πR²/360
For 110° ............................... πR²*110/360 =50(units squared)

R²=50*360/(110π)
==>R=6*√(50/(11π))≈7,217137....(units)

Answer 2

Area of the sector(A) is given by:

`A = \pi r^2 \cdot (\theta)/(360^(\circ))`

where,

r is the radius of the circle and
`\theta` is the central angle in degree.

As per the statement:

The area of the sector formed by the 110 degree central angle is 50 units squared.

⇒A = 50 units squared and
`\theta = 110^(\circ)`

Substitute these in [1] and use 3.14 for pi we have;

`50 = 3.14 \cdot r^2 \cdot (110)/(360)`

⇒
`50 = 0.959444446r^2`

Divide both sides by 0.959444446 we get;

`r^2 = 52.1134915`

⇒
`r = √(52.1134915)`

Simplify:

r ≈ 7.22 units

Therefore, the radius of this circle is, 7.22 units