The angle of a sector of a circle is 108°. If the radius of the circle is 31/2cm, find the perimeter of the sector
Answer Details
A sector of a circle is a region bounded by two radii and an arc. The perimeter of a sector is the sum of the arc length and the lengths of the two radii.
In this case, we are given that the angle of the sector is 108° and the radius of the circle is 31/2 cm.
To find the arc length, we need to know the circumference of the entire circle, which is given by 2πr, where r is the radius of the circle. So, the circumference of the circle is 2π(31/2) cm = 31π cm.
The angle of the sector is 108°, which is 108/360 or 3/10 of the entire circle. So, the arc length of the sector is (3/10) × 31π cm = 9.3π cm.
The two radii of the sector have length 31/2 cm each.
Therefore, the perimeter of the sector is the sum of the arc length and the two radii, which is 9.3π cm + 31/2 cm + 31/2 cm = (9.3π + 31) / 2 cm.
This is approximately equal to 13.6 cm. Therefore, the answer is (E) 13 3/5 cm.