What is the radius of a circle if intercepted arc is and the area of the sector is 28.125nsq.ft. ?
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
Round the answer to the hundredth place.
![**Question:**
What is the radius of a circle if the intercepted arc is \(\frac{\pi}{4}\) and the area of the sector is \(28.125\pi \, \text{sq. ft.}\)?
**Diagrams and Explanation:**
There are no graphs or diagrams accompanying this question. The problem consists of calculating the radius of a circle given specific conditions related to the circle's arc and sector area.
In this context, the sector's area formula is defined as:
\[
\text{Area of Sector} = \frac{\theta}{2\pi} \times \pi r^2
\]
where \(\theta\) is the angle of the arc in radians and \(r\) is the radius.
Given variables:
- \(\theta = \frac{\pi}{4}\)
- \(\text{Area of Sector} = 28.125\pi \, \text{sq. ft.}\)
The task is to solve for \(r\), the radius of the circle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ed323b9-8e35-4824-8e78-fcaf55c6ad57%2F1aeaaaab-c6dd-40da-8687-d752c7e478bf%2Fwohhu5e_processed.jpeg&w=3840&q=75)
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