Question

The area of a sector of a circle with a radius measuring 15 cm is 235.62 cm^2 . What is the measure of the central angle, to the nearest degree that forms the sector?

Answer 1

120°

Explanation:

The area of a sector of a circle is given by:

`A = (\alpha )/(360) * \pi r^2`

where α = central angle of sector in degrees

r = radius of circle.

The radius of the circle is 15 cm and the area of the sector is 235.62 cm^2. Therefore:

`235.62 = (\alpha )/(360) * \pi * 15^2\\\\84823.2 = 706.86 * \alpha \\\\=> \alpha = 84823.2 / 706.86\\\\\alpha = 120^o`

The central angle of the sector is 120°