Question

calculator
the area of this circle is 72π m².
what is the area of a 45° sector of this circle?
8πm²
9πm²
12π m²
18π m²

Explanation:

Step1: Find the proportion of the sector

The proportion of a \(45^{\circ}\) sector in a full - circle (\(360^{\circ}\)) is \(\frac{45}{360}=\frac{1}{8}\).

Step2: Calculate the area of the sector

Given the area of the circle \(A = 72\pi\space m^{2}\). The area of the sector \(A_{sector}\) is the proportion of the sector times the area of the circle. So \(A_{sector}=\frac{1}{8}\times72\pi\).

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Answer:

\(9\pi m^{2}\) (the second option)