The angle of a sector of a circle radius 10.5 cm is 48o. Calculate the perimeter of the sector.
Answer Details
The perimeter of a sector of a circle is equal to the circumference of the circle that is part of the sector plus the length of the arc of the sector. To calculate the perimeter of a sector, we need to find the length of the arc and the circumference of the circle first.
The length of the arc is given by the formula:
Arc length = (Angle of sector / 360) x Circumference of the circle
The circumference of a circle is given by the formula:
Circumference = 2 * pi * radius
Plugging in the values we have, the circumference of the circle is 2 * pi * 10.5 = 65.97 cm.
The length of the arc is (48 / 360) x 65.97 = 12.19 cm.
Adding the length of the arc to the circumference of the circle, we get 65.97 + 12.19 = 78.16 cm, which is the perimeter of the sector.
Therefore, the answer is 78.16 cm, which is closest to 29.8cm.