The perimeter of a minor sector of a circle of radius 4 units subtending an angle of 45° is:
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 8 + π units.
The length of the arc of a minor sector of a circle is given by the formula:
Arc length = (θ/360) × 2πr
where θ is the angle subtended by the arc at the center of the circle, and r is the radius of the circle.
In this case, θ = 45° and r = 4 units. Substituting these values into the formula, we get:
Arc length = (45/360) × 2π × 4
Arc length = (1/8) × 8π
Arc length = π units
The perimeter of the minor sector is the sum of the arc length and the lengths of the two radii. Since the radii are equal to 4 units each, the total length of the radii is 4 + 4 = 8 units.
Therefore, the perimeter of the minor sector is:
Perimeter = Arc length + 2r
Perimeter = π + 8