Question

2. The central angle of the sector of a circle is 45° and its radius is 14cm. Find
the length of the arc, area and the perimeter of the sector.​

Answer 1

$\huge{ \sf{ \underbrace{ \underline{given}}}}$

The central angle of the sector of a circle is

45° and its radius is 14cm

$\huge{ \sf{ \underbrace{ \underline{to \: find}}}}$

Length of arc = ?

Area and Perimeter of sector = ?

$\huge{ \sf{ \underbrace{ \underline{answer}}}}$

$radius \: of \: sector \: = 14cm \\ central \: angle \: of \: sector = 45 \\ \implies \: length \: of \: arc = \frac{ \theta}{360} \times 2\pi \: r \\ \implies \: \frac{45}{360} \times 2\pi \: r \\ \implies \: \frac{45}{360} \times 14 \\ \implies \: \frac{1}{8} \times 2 \times \frac{22}{7} \times 14 \\ \implies \: length \: of \: arc = 11cm$

$perimeter \: of \: a \: sector = 2r + \\ length \: of \: arc \\ \implies \: 2r + length \: of \: arc \\ \implies2(14) + 11 \\ 28 + 11 = 39cm$

$area \: of \: sector \\ \frac{ \theta}{360} \times \pi \: r {}^{2} \\ \implies \frac{45}{360} \times \frac{22}{7} (14) {}^{2} \\ \implies\frac{1}{8} \times \frac{22}{7} \times (14 \times 14) \\ \implies area \: of \: sector = 77cm {}^{2}$