Answer:
Area of the sector(A) is given by:
\(A = \pi r^2 \cdot \frac{\theta}{360^{\circ}}\)
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;
\(50 = 3.14 \cdot r^2 \cdot \frac{110}{360}\)
⇒\(50 = 0.959444446r^2\)
Divide both sides by 0.959444446 we get;
\(r^2 = 52.1134915\)
⇒\(r = \sqrt{52.1134915}\)
Simplify:
r ≈ 7.22 units
Therefore, the radius of this circle is, 7.22 units
