Find the area of a sector of a circle having radius r and central angle $$\theta$$ . If necessary, express the answer to the nearest
tenth.
-Find the measure (in radians) of a central angle of a sector of area 56 square inches in a circle of radius 8 inches. Round to the nearest hundredth.
A) 1.75 radians
B) 0.88 radians
C) 2.63 radians
D) 3.50 radians

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 $A$ is the area, $r$ is the radius, and $\theta$ is the central angle in radians. Given $A = 56$ square inches and $r = 8$ inches, we can solve for $\theta$: $56 = \frac{1}{2} \times 8^2 \times \theta$. Simplifying, we get $\theta = 1.75$ radians.

Find the Area of a Sector of a Circle Having θ\thetaθ

Find the Area of a Sector of a Circle Having $\theta$