Find the area of a sector of a circle having radius r and central angle θ. If necessary, express the answer to the nearest
tenth.
-$$\mathrm { r } = 6.4 \mathrm { mi } , \theta = 36 ^ { \circ }$$
A) $12.9 \mathrm { mi } ^ { 2 }$
B) $25.7 \mathrm { mi } ^ { 2 }$
C) $0.6 \mathrm { mi } ^ { 2 }$
D) $2.0 \mathrm { mi } ^ { 2 }$

Question

Quizplus · Accepted Answer

The area of a sector of a circle is given by the formula $ \frac{1}{2} r^2 \theta $, where $ r $ is the radius and $ \theta $ is the central angle in radians. First, convert $ \theta $ from degrees to radians: $ \theta = 36^\circ = \frac{36}{180} \pi = \frac{\pi}{5} $ radians. Then, calculate the area: $ \frac{1}{2} \times (6.4)^2 \times \frac{\pi}{5} = 12.9 $ square miles, to the nearest tenth.

Find the Area of a Sector of a Circle Having r=6.4mi,θ=36∘\mathrm { r } = 6.4 \mathrm { mi } , \theta = 36 ^ { \circ }r=6.4mi,θ=36∘

Find the Area of a Sector of a Circle Having $\mathrm { r } = 6.4 \mathrm { mi } , \theta = 36 ^ { \circ }$