Question

The formula for finding the length of an arc on a circle is L=2πr(x360) , where r is the radius of the circle and x is the measure of the central angle of the arc. Solve for r. r=xL720π r=720πxL r=πx180L r=180Lπx

Answer 1

The formula for length of an arc on a circle is given by the formula:

$L = \frac{2 \pi rx}{360}$,

where 'r' is the radius of the circle and 'x' is the measure of the central angle of the arc.

We have to determine the value of radius 'r'.

Since, $L = \frac{2 \pi rx}{360}$

By Cross multiplication, we get

$360 \times L = 2 \pi rx$

$\frac{360 \times L}{ 2 \pi x} =r$

$\frac{180 \times L}{ \pi x} =r$

$r = \frac{180L}{ \pi x}$

Therefore, the radius 'r' is given by $r = \frac{180L}{ \pi x}$.

Option 4 is the correct answer.

Answer 2

I got the opposite of this answer, it was instead "solve for x."

With anyone with this for their question, the answer is the opposite:

x = 180L/$\pi$r

Thus x = 180L/pi r, looks just like D, but the "r" and "x" placements are switched.