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

L = 16 [in]

Step-by-step explanation:

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

`A = (\alpha*r^(2) )/(2) \\where:\\A= area = 64[in^(2)]\\r = radius = 8[in]\\\\\alpha = angle[rad]therefore\\\alpha =(2*A)/(r^(2) ) \\\alpha =(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]`