Question

Circle $O$ has radius of $10$, how do you find the length of an arc subtended by a central angle measuring $1.5$ radians?

Answer 1

Hint: As per the given question we have to find the length of the arc, with the radius given. We know that a circle is a two dimensional figure formed by a set of all those points which are equidistant from a fixed point in the same plane. That fixed point is called the centre of the circle while the fixed distance from the centre of the circle is called the radius of the circle. And we know that the line that passes through the centre and touches the circumference on both sides of the circle is called the diameter.

Complete step by step solution:
In the given question we have the radius which is $10$.
We know the relation between the radius, angle and the length of the arc which is length of arc is equal to the product of the radius and the angle subtended i.e. $s = r \times \theta $ , where $s$ is the length of the arc, $r$ is the radius and $\theta $ as the angle.
Now applying the formula and putting the values: $s = 10 \times 1.5$ i.e. $15units.$

Hence the length of the arc drawn is $15$units.

Note: In this type of question we should remember the definition of radius and arc of the circle and also the relation between them. We can also solve this question by another method which is length of arc$ = $circumference$ \times $ fraction of circle, where the value of circumference is $2\pi r$ and fraction of the circle in this question is $\dfrac{{1.5}}{{2\pi }}$.