Question

use the diagram to answer the questions.
what is the area of the circle in terms of pi?
π units²
what is the measure of the central angle of the shaded
sector?
°
what is the area of the shaded sector rounded to the
nearest whole number?
units²

Explanation:

Step1: Calculate the area of the circle

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(r = 11\), then \(A=\pi\times11^{2}=121\pi\)

Step2: Find the central angle of the shaded sector

The total angle in a circle is \(360^{\circ}\). If one non - shaded angle is \(217^{\circ}\), then the central angle of the shaded sector \(\theta=360^{\circ}- 217^{\circ}=143^{\circ}\)

Step3: Calculate the area of the shaded sector

The formula for the area of a sector is \(A=\frac{\theta}{360}\times\pi r^{2}\). Substitute \(\theta = 143^{\circ}\) and \(r = 11\) into the formula:

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Answer:

The area of the circle is \(121\pi\) units². The measure of the central angle of the shaded sector is \(143^{\circ}\). The area of the shaded sector is \(151\) units².