The arc length of the partial circle is 7.5π
Calculating arc length
From the question, we are to determine the arc length of the partial circle
The length of an arc can be calculated by using the formula
[tex]l = \frac{\theta}{360^\circ} \times 2\pi r[/tex]
Where [tex]l[/tex] is the length of the arc
[tex]\theta[/tex] is the angle subtended
and r is the radius
From the diagram,
θ = 270°
r = 5
Putting the values into the equation, we get
[tex]l = \frac{270 ^\circ}{360^\circ} \times 2\pi \times 5[/tex]
[tex]l = \frac{3}{4} \times 2\pi \times 5[/tex]
[tex]l = \frac{30\pi}{4}[/tex]
[tex]l = \frac{15}{2}\pi[/tex] OR 7.5π
Hence, the arc length of the partial circle is 7.5π
Learn more on Calculating arc length here: https://brainly.com/question/16552139
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