Question

How do you find the length of the arc (to the nearest tenth) of a circle of radius \[6.8\] in that subtends a central angle of \[\dfrac{\pi }{8}\] ?

Answer 1

Hint: Here the above question is based on finding the length of the arc. Since, we are given a radius \[r\] of circle and central angle \[\theta \] so we will find the length of the arc by applying the formula and \[l = r \times \theta \] where \[l\] stands for length of the arc. Lastly we will substitute the given values in it and perform the required calculations.
Formula: The formula used for finding the arc length of the circle in the above question is
 \[l = r \times \theta \]
Where \[l\] stands for length of the arc, \[r\] stands for the radius of the circle and \[\theta \] represents the central angle in radians.

Complete step-by-step answer:
As in the above question we are asked to find the length of the arc (to the nearest tenth) of a circle of radius \[6.8\] subtending a central angle of \[\dfrac{\pi }{8}\]
So we will apply the formula \[l = r \times \theta \]
 \[
   \Rightarrow 6.8 \times \left( {\dfrac{\pi }{8}} \right) \\
   \Rightarrow 2.67035 \;
 \]
Now as we are asked to find the length of the arc to the nearest tenth so the answer will be \[2.7\] units.
So, the correct answer is “\[2.7\] units.”.

Note: An arc is basically a portion of circumference of a circle while the length of an arc is basically the length of its portion of circumference. Lastly value of \[\pi \] as \[3.14\] is always preferred
Notes: Keep in mind that when we solve such types of problems try to make the required calculations in the equation for getting a final solution. Avoid any calculation mistakes due to sign conventions and converting degree into radians.. Make sure to calculate the final answer for the unit as it is asked in the question like in the above question it is asked to calculate the answer to the nearest tenth so the final answer was \[2.7\] units.