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What is the perimeter of a sector of a circle (in cm) if the radius of the circle is 10.5 cm and the angle subtended at the centre of the circle is 60°? (Use π=722)
32
41
22
35
32
Calculate the arc length by multiplying the circumference (2πr = 66) by the fraction (60/360 = 1/6) to get 11. Then add 2 times the radius (10.5 + 10.5 = 21) to get the total perimeter (11 + 21 = 32).
Radius of the circle (r) = 10.5 cm, central angle (θ) = 60°, and π = 22/7.
P=2r+360°θ×2πr
Calculate the arc length by multiplying the circumference (2πr = 66) by the fraction (60/360 = 1/6) to get 11. Then add 2 times the radius (10.5 + 10.5 = 21) to get the total perimeter (11 + 21 = 32).
A common mistake is calculating only the arc length (11 cm) and forgetting to add the two bounding radii of the sector.
Calculate the Arc Length
The formula for the length of an arc is L=360°θ×2πr. Substituting the given values: L=360°60°×2×722×10.5=61×2×22×1.5.
L=11 cm
Calculate the Total Perimeter
The perimeter of a sector includes the arc length plus the two radii that form the sides of the sector: P=L+2r.
P=11+2(10.5)=11+21=32 cm
A is correct because the sum of the arc length (11 cm) and the two radii (21 cm) equals 32 cm.
This concept frequently appears in Mensuration problems; remember that 'perimeter of a sector' always includes the two radial segments, unlike just the arc length.
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