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.
-$r = 39.7$ centimeters, $\theta = \frac { \pi } { 14 }$ radians, $A =$ ?
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 the formula $A = \frac { 1 } { 2 } r ^ { 2 } \theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. Substituting the given values into the formula, we get:$$A = \frac { 1 } { 2 } (39.7 \mathrm {~cm} ) ^ { 2 } \left( \frac { \pi } { 14 } \mathrm {~rad} \right) \approx 176.8 \mathrm {~cm} ^ { 2 }$$Therefore, the missing quantity is $A = 176.8 \mathrm {~cm} ^ { 2 }$.

If a Denotes the Area of the Sector of a Circle