Question

A circular sector has an area of 64 in. squared. The radius of the circle is 8 in. What is the arc length of the​ sector?

Answer 1

Answer:

L = 16 [in]

Explanation:

In order to find the arch we must first find the angle that forms the circular sector, using the following formula:

$A = \frac{\alpha*r^{2} }{2} \\where:\\A= area = 64[in^{2}]\\r = radius = 8[in]\\\\\alpha = angle[rad]therefore\\\alpha =\frac{2*A}{r^{2} } \\\alpha =\frac{2*64}{8^{2} } \\\alpha =2[rad]$

Now using the following equation we can calculate the arc length

$L=\alpha *r\\L=2*8\\L=16[in]$