Formula for the length of an arc of a circle

Posted By Admin @ September 03, 2022


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


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.

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