If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.
-$\mathrm { r } = 39.7$ centimeters, $\theta = \frac { \pi } { 14 }$ radians, $\mathrm { A } =$ ?
A) $176.8 \mathrm {~cm} ^ { 2 }$
B) $56.3 \mathrm {~cm} ^ { 2 }$
C) $4.5 \mathrm {~cm} ^ { 2 }$
D) $353.6 \mathrm {~cm} ^ { 2 }$

Question

Quizplus · Accepted Answer

The area of a sector of a circle is given by $A = \frac{1}{2} r^2 \theta$, where $r$ is the radius and $\theta$ is the central angle in radians. Substituting $r = 39.7$ cm and $\theta = \frac{\pi}{14}$ into the formula gives $A = \frac{1}{2} \times 39.7^2 \times \frac{\pi}{14} \approx 176.8 \, \mathrm{cm}^2$.

If a Denotes the Area of the Sector of a Circle