The length of the inscribed arc is given by option b. 3.14 inches.
What is arc length of a circle?
"The length of the inscribed arc of a circle is the distance between two points along a section of a curve."
What is central angle of a circle?
"The central angle of a circle is the angle between two radii of a circle."
Formula to calculate the length of the inscribed arc:
\(s=r\) × \(\theta\)
where \(s\) represents the length of the inscribed arc
\(r\) is the radius of the circle
\(\theta\) represents the central angle of a circle in radians
Formula to convert angle in degrees to radians:
Ф = ∅ × (π/180)
where, ∅ is the angle measured in degrees
Ф is the angle measured in radians.
From given data,
\(r=4\) inches
\(\theta=45\)
So, the central angle in radians is:
⇒ \(\theta=45\) × \(\frac{\pi}{180}\)
⇒ \(\theta=\frac{\pi}{4}\)
And the length of the inscribed arc is: \(s=r\) × \(\theta\)
⇒ \(s=4\) × \(\frac{\pi}{4}\)
⇒ \(s=\pi\)
⇒ \(s=3.14\) inches
So, the length of the inscribed arc is 3.14 inches.
Hence, the correct answer is option b. 3.14 inches.
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