Answer:
<em>The perimeter of the pizza slice is 20.1 cm</em>
Step-by-step explanation:
<u>Perimeter of a Sector of a Circle</u>
The arc length of a sector of a circle of radius r and angle θ is given by:
L = rθ
The angle must be expressed in radians.
The total perimeter of the circular sector, including the two radii, is:
P = rθ + 2r
The pizza slice has a radius of r=7 cm and a central angle of θ=50°
Converting to radians:
The perimeter is:
Calculating:
P = 20.1 cm
The perimeter of the pizza slice is 20.1 cm
Let AB be a chord of the given circle with centre and radius 13 cm.
Then, OA = 13 cm and ab = 10 cm
From O, draw OL⊥ AB
We know that the perpendicular from the centre of a circle to a chord bisects the chord.
∴ AL = ½AB = (½ × 10)cm = 5 cm
From the right △OLA, we have
OA² = OL² + AL²
==> OL² = OA² – AL²
==> [(13)² – (5)²] cm² = 144cm²
==> OL = √144cm = 12 cm
Hence, the distance of the chord from the centre is 12 cm.
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