Question

Find the length of an arc of semicircle?

Answer 1

Hint: Find the arc length by applying the formula to the supplied radius of $$r=10$$ cm. Arc length $$={\displaystyle \frac{\theta }{{360}^{\circ }}}\times 2\pi r$$, where r is the radius and $$\theta$$ is the central angle.

Complete step-by-step solution:
The diameter of a circle is defined as the diameter of a circle measured from the center to another point on the circle in the query.
The radius of a circle is the distance between the center and the perimeter of a circle.
As a result, the radius of the circle in the question is $$r=10$$ cm.
The arc of a circle is a section of the circle's circumference.
Here, we must determine the length of the arc that forms $${180}^{\circ }$$ angle with the center.
That is, if the two arc end points are added together with the center, the resulting angle is $${180}^{\circ }$$.
We already know that the arc length, radius, and angle all have a relationship.
Arc length $$={\displaystyle \frac{\theta }{{360}^{\circ }}}\times 2\pi r$$
Here, r is the radius of the circle which is 10 cm here.
Angle$$\theta$$ is the corresponding angle, which is $${180}^{\circ }$$ here.
Therefore, the arc length is
$$={\displaystyle \frac{{180}^{\circ }}{{360}^{\circ }}}\times 2\pi \times 10={\displaystyle \frac{1}{2}}\times 20\pi =10\pi$$
Hence the arc length is $$10\pi$$ cm or we can put the value of $$\pi ={\displaystyle \frac{22}{7}}$$
The arc length is $$=10\times {\displaystyle \frac{22}{7}}={\displaystyle \frac{220}{7}}\text{cm}$$.

Note: Alternatively we can say that, since the corresponding central angle of the arc is $${180}^{\circ }$$, which half of is $${360}^{\circ }$$, the arc is essentially a semicircle without the diameter. An arc is the part of a circle which is formed due to a particular angle.