Find the perimeter of major sector of a circle of radius 12 metres, whose minor sector subtends an angle of 75° at the centre.

24 + 19π metres

Formula Used

Perimeter of major arc = 2 x \(\Pi \) x r x \(\theta \)/360 + 2r

Where \(\theta \) = 360 - angle subtended by minor arc

Calculations

Here, we have radius of the circle = 12 m and minor sector angle subtends an angle = \({75}^\circ\)

Angle subtended by major arc = \({360}^\circ\) - \({75}^\circ\) = \({285}^\circ\)

Perimeter of major arc = 2 x \(\Pi \) x 12 x 285/360 + 2 x 12

= 19\(\Pi \) + 24 metres

Therefore, Perimeter of major arc is 19\(\Pi \) + 24 metres