Question

Find the area of a circle with an arc length of 4π and a central angle of 45 degrees. Leave the answer in terms of π.

Answer 1

`~~~~~~\text{Arc length} = r \theta \\\\\implies 4\pi = r\left( 45 * (\pi)/(180) \right)~~~~~~~~;[\theta ~ \text{is in radians.}]\\\\\implies 4 = (45r)/(180)\\\\\implies 45r = 180 * 4 = 720\\\\\implies r = (720)/(45)\\\\\implies r = 16~ \text{units.}\\\\\text{Now,}\\\\\text{Area} = \pi r^2\\\\~~~~~~~=\pi \cdot 16^2\\\\~~~~~~~=256\pi~ \text{units}^2`