Question

If perimeter of a sector of a circle of radius 7 cm is 16.2 cm find the central angle of the sector

Answer 1

Step-by-step explanation:

$Perimeter \: of \: sector \: of \: circle \: = r + r + l \\ \therefore \: r + r + l = 16.2 \\ 7 + 7 + l = 16.2 \\ 14 + l = 16.2 \\ l = 16.2 - 14 \\ l = 2.2 \: cm \\ now \: let \: the \: central \: angle \: be \: \theta \\ \therefore l = \frac{ \theta}{360 \degree} \times 2 \pi \: r \\ 2.2 = \frac{ \theta}{360 \degree} \times 2 \times \ \frac{22}{7} \times \: 7 \\ 2.2 = \frac{ \theta}{360 \degree} \times 2 \times \ 22 \\ \theta = \frac{2.2 \times 360}{2 \times 22} = \frac{22 \times 36}{2 \times 22} \\ \theta =18 \degree \\ thus \: the \: measure \\ \: of \: central \: \angle \: = 18 \degree$