Question

A circle with a diameter of 10 inches is spanned by a central angle of 180 degrees. What is the length of the subtended arc?

Answer 1

since the diameter of the circle is 10, then its radius must be half that or 5.

`\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=&5\\ \theta=&180 \end{cases}\implies s=\cfrac{\pi (180)(5)}{180}\implies s=5\pi \implies s\approx 15.71`

Answer 2

The correct answer is 15.7 inches

Explanation:

Points to remember

Circumference of a circle = 2πr

Where r is the radius of circle

To find the value of arc length

It is given that, diameter = 10 inches

Radius = diameter/2 = 10/2 = 5 inches

Circumference = 2πr

= 2 * 3.14 * 5

= 31.4

central angle of arc =180

Arc length = (180/360) * circumference

= (1/2) * 31.4

= 15.7 inches

Therefore the correct answer is 15.7 inches