Question

A circle has an arc length of 2π in.
The central angle for this arc measures π/6 radians.
What is the area of the associated sector?

(Remember to show formulas/equations and numbers in those formulas/equations to receive credit. Also, make sure your final answer is in EXACT form and includes units!)

Answer 1

Answer:

12π

Step-by-step explanation:

should be ur answer

Answer 2

The area of sector is 37.68 square inches

Solution:

Given that,

$Arc\ length = 2\pi \text{ inches }$

$central\ angle = \frac{ \pi }{6} \text{ radians }$

To find: area of sector

The arc length formula is:

$s = r \times \theta\\\\2 \pi = r \times \frac{ \pi }{6}\\\\r = 12$

The area of sector of circle is given as:

$Area = \frac{ \theta }{ 2 \pi } \times \pi r^2\\\\Area = \frac{ \frac{ \pi }{ 6 }}{2 \pi } \times \pi \times 12^2\\\\Area = \frac{ \pi }{12} \times 144\\\\Area = 3.14 \times 12\\\\Area =37.68$

Thus area of sector is 37.68 square inches

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