Question

6 - 7. what is the area of the sector air?
8 - 9 what is the area of the sector yis?

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle of the sector and \(r\) is the radius of the circle.

Step2: Calculate the area of sector AIR

For sector AIR, \(\theta = 150^{\circ}\) and \(r = 6\mathrm{cm}\).
Substitute into the formula:
\(A_{AIR}=\frac{150}{360}\times\pi\times6^{2}\)
\(=\frac{150}{360}\times\pi\times36\)
\(= 15\pi\)
\(\approx15\times3.14 = 47.1\mathrm{cm}^{2}\)

Step3: Calculate the area of sector YIS

For sector YIS, \(\theta = 45^{\circ}\) and \(r = 7\mathrm{cm}\).
Substitute into the formula:
\(A_{YIS}=\frac{45}{360}\times\pi\times7^{2}\)
\(=\frac{45}{360}\times\pi\times49\)
\(=\frac{49\pi}{8}\)
\(\approx\frac{49\times3.14}{8}=\frac{153.86}{8}=19.2325\mathrm{cm}^{2}\)

Answer:

The area of sector AIR is approximately \(47.1\mathrm{cm}^{2}\). The area of sector YIS is approximately \(19.23\mathrm{cm}^{2}\).