Solve the problem.
-Find the radius of a circle in which a central angle of $\frac { \pi } { 3 }$ radian determines a sector of area 56 square meters. Round to the nearest hundredth.
A) $10.34 \mathrm {~m}$
B) $14.63 \mathrm {~m}$
C) $7.31 \mathrm {~m}$
D) $106.95 \mathrm {~m}$

Question

Quizplus · Accepted Answer

The area of a sector of a circle is given by $ \frac{1}{2} r^2 \theta $, where $ r $ is the radius and $ \theta $ is the central angle in radians. Given $ \theta = \frac{\pi}{3} $ and the area of the sector as 56 square meters, we can solve for $ r $ as follows: $ 56 = \frac{1}{2} r^2 \left(\frac{\pi}{3}\right) $. Solving for $ r $, we find $ r \approx 10.34 $ meters.

Solve the Problem π3\frac { \pi } { 3 }3π​ Radian Determines a Sector of Area 56 Square Meters

Solve the Problem $\frac { \pi } { 3 }$ Radian Determines a Sector of Area 56 Square Meters