Question

The diameter of a circle is 10 cm , then find the length of the arc when the corresponding central angle is ${180}^{\circ }(\pi =3.14)$ ?
A. 15.7
B. 16
C. 3.14
D. 18

Answer 1

Hint: Using the given diameter we can get the radius of the circle as the radius is half of the diameter and when the central angle is given the length of the arc is given by the formula $Length={\displaystyle \frac{\theta }{360}}\times 2\pi r$ and using the given values we get the required length.

Complete step by step solution:
We are given a circle and it is given that the diameter of the circle is 10 cm
We know that the radius of the circle is given by half of its diameter.
Hence the radius of the given circle is given by
$\Rightarrow r={\displaystyle \frac{d}{2}}={\displaystyle \frac{10}{2}}=5cm$
Now we have the radius of the circle
Now we are asked to find the length of the arc corresponding to the central angle
Whenever the central angle is given the length of the arc is given by the formula
$\Rightarrow Length={\displaystyle \frac{\theta }{360}}\times 2\pi r$
Where $\theta$ is the central angle and r is its radius
Here the central angle is ${180}^{\circ }$ and radius is 5 cm
$$\begin{gathered} \Rightarrow Length={\displaystyle \frac{180}{360}}\times 2\times 3.14\times 5 \\ \Rightarrow Length={\displaystyle \frac{1}{2}}\times 2\times 3.14\times 5 \\ \Rightarrow Length=3.14\times 5=15.7 \end{gathered}$$
Hence we get the length of the arc to be 15.7 units

Therefore the correct answer is option A.

Note :
1) A part of a curve or a part of a circumference of a circle is called Arc.
2) In general, the length of a curve is called the arc length.
3) An arc length is measured by taking a part of the whole circle.