Question

6 - 7. what is the area of the sector air?
8 - 9 what is the area of the sector yis?
6 - 7. format: (answer) pi *
your answer
this is a required question
8 - 9. format: (answer) pi *
your answer

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 and \(r\) is the radius.

Step2: Solve for sector AIR

For sector AIR, \(\theta = 150^{\circ}\) and \(r = 6\mathrm{cm}\).
Substitute into the formula: \(A=\frac{150}{360}\times\pi\times6^{2}\)
Simplify \(\frac{150}{360}=\frac{5}{12}\) and \(6^{2}=36\)
\(A=\frac{5}{12}\times\pi\times36\)
\(A = 15\pi\)

Step3: Solve for sector YIS

For sector YIS, \(\theta = 45^{\circ}\) and \(r = 7\mathrm{cm}\)
Substitute into the formula: \(A=\frac{45}{360}\times\pi\times7^{2}\)
Simplify \(\frac{45}{360}=\frac{1}{8}\) and \(7^{2} = 49\)
\(A=\frac{1}{8}\times\pi\times49=\frac{49}{8}\pi\)

Answer:

6 - 7. \(15\pi\)
8 - 9. \(\frac{49}{8}\pi\)