Question

A circle has a circumference whose length is 25pi. Find the length of an arc whose central angle is 90 degrees.

Answer 1

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we are given that the circumference is 25π. Solving for the radius, we get:

25π = 2πr

r = 25/2

The length of an arc whose central angle is 90 degrees can be found using the formula:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle in degrees, and r is the radius. Substituting the given values, we get:

L = (90/360) × 2π(25/2)

L = (1/4) × 25π

L = 25π/4

Therefore, the length of the arc is 25π/4.

Answer 2

`(25)/(4) \pi` or 19.6350.

Explanation:

So we can think about the length of the circumference of this circle at the length of anc arc of 360° for this circle. Then, in order to find the length of an arc of 90° you can use a conversion factor to calculate it. This is how you do it:

`90(deg)*(25\pi )/(360(deg)) =\\ \\(90)/(360)(deg)*25\pi =\\ \\(1)/(4)* 25\pi =\\ \\(25)/(4) \pi =19.6350`