What is the length of the arc of the sector of a circle with radius 14cm and of central angle 90 degree ?

(a) 22cm
(b) 44cm
(c) 88cm
(d) 11cm

This question is about the length of the arc of a sector of a circle. The circle has a radius of 14 cm and the central angle is 90 degrees. There are four answer choices: 22 cm, 44 cm, 88 cm, and 11 cm.

The correct answer is 22 cm.

We can find the length of the arc by following these steps:

1. Calculate the circumference of the circle.
2. Find the ratio between the sector’s central angle θ and 360 degrees.
3. Multiply the circumference of the circle by the ratio you just found.

Here’s how this works for the problem :

• The circumference of the circle is

c=2πr

c=2π(14cm)

c=28πcm

• The ratio between the sector’s central angle θ (which is 90 degrees) and 360 degrees is

sector angle =θ/360∘

sector angle = 90∘/360∘

sector angle =1/4

• The length of the arc is

=c×(θ/360∘)

=28πcm×(1/4)

=7πcm

Since π is an irrational number, we can’t get an exact answer in centimeters. However, in these type of problems, it’s common practice to assume the circle is perfectly round and use 22/7 for π instead.

Using 22/7 for π,

we get an arc length of

Arc Length =7×(22/7)

Arc Length =22cm.

This is the answer choice (a).