Question

A circle has a circumference whose length is 25 find the length of arc whose central angle 90

Answer 1

There are 360° in a circle. So, A 90° central angle cuts off an arc which has length 90/360 = 1/4 of the circumference.

Therefore, length of arc = (1/4)(25π) = 25π/4.

Explanation:

Answer 2

Question:

A circle has a circumference whose length is 25pi find the length of arc whose central angle 90°

Answer:

The length of arc is 19.625 units

Solution:

Given that,

central angle = 90 degree

Circumference =
`25 \pi`

We know that,

`circumference\ of\ circle = 2 \pi r`

Therefore,

`25 \pi = 2 \pi r\\\\r = (25)/(2) = 12.5`

The formula for arc length when angle is in degrees is:

`\text{ Arc length } = 2 \pi r * (\theta)/(360)`

Substituting the given values,

`\text{Arc Length } = 2* 3.14 * 12.5 * (90)/(360)\\\\\text{Arc length } = 78.5 * (1)/(4)\\\\\text{Arc Length } = 19.625`

Thus length of arc is 19.625 units