Calculate the perimeter of a sector of a circle of radius 9cm and angle 36o.
Answer Details
The perimeter of a sector of a circle is the sum of the arc length and the two radii. To find the perimeter, we need to first find the arc length using the formula:
arc length = (angle/360) x 2 x π x radius
In this case, the angle is given as 36°, the radius is given as 9cm, and π is approximately equal to 3.14. Substituting these values into the formula, we get:
arc length = (36/360) x 2 x 3.14 x 9 = 2.83 cm (rounded to two decimal places)
Now, we can find the perimeter by adding the two radii to the arc length:
perimeter = 2 x 9 + 2.83 = 20.83 cm
Therefore, the answer is (B) (18 + 9π/5) cm, rounded to two decimal places.