Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

The radius of a certain circle is 30 cm. Find the approximate length of an arc of this circle; if the length of the chord of the arc be 30 cm.

Answer
VerifiedVerified
486k+ views
like imagedislike image
Hint:
Here we need to find the approximate length of an arc of this circle. For that, we will draw a chord in a circle and we will join the end points of this chord to the center of this circle which will form a triangle, and the triangle formed will be an equilateral triangle. From there, we will get the angle made by the arc at the center and then we will use the formula to find the length of the arc.

Complete step by step solution:
First we will draw a chord in a circle and we will join the end points of this chord to the center of this circle which will form a triangle.
seo images

We can see from the figure,
AO=B0=30cm as these are the radii of the same circle.
The triangle formed is an equilateral triangle as all the sides are equal and thus the each angle of a triangle is equal to 60.
Thus, AOB=60
Now, we will find the length of the arc formed corresponding to that chord.
We know the formula to find the length of arc is given by
length of arc=θ360×2πr
Here θ is the angle made by the arc at the center and r is the radius of the circle.
Substituting the value of angle and radius of the circle, we get
length of arc=60360×2×227×30
On multiplying the terms, we get
length of arc=31.42cm

Thus, the required length of the arc is equal to 31.42 cm.

Note:
Here we have calculated the length of an arc formed. An arc of a circle is defined as the part or portion of the circumference of the circle. The formula to find the length of arc is equal to the product of circumference of circle and the ratio of angle made by the arc to the total angle i.e.
length of arc=θ360×2πr.