Question

in circle n with (mangle mnp = 96^{circ}) and (mn = 11), find the area of sector mnp. round to the nearest hundredth.

Explanation:

Step1: Recall area - of - circle formula

The area of a circle is $A = \pi r^{2}$. Here, the radius $r = MN=11$, so the area of circle $N$ is $A=\pi\times11^{2}=121\pi$.

Step2: Recall sector - area formula

The formula for the area of a sector of a circle with central angle $\theta$ (in degrees) is $A_{sector}=\frac{\theta}{360}\times A_{circle}$. Given $\theta = 96^{\circ}$ and $A_{circle}=121\pi$.

Step3: Calculate the area of the sector

$A_{sector}=\frac{96}{360}\times121\pi=\frac{8}{30}\times121\pi=\frac{8\times121\pi}{30}=\frac{968\pi}{30}\approx\frac{968\times3.14159}{30}\approx101.73$.

Answer:

$101.73$