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Find the area of a sector of a circle with radius 14 cm, if the length of the corresponding arc is 22 cm.

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154 sq. cm

164 sq. cm.

150 sq. cm

148 sq.cm.

answer is A.

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Detailed Solution

Given,
Circle Radius

r = 14 cm

Arc Length

l = 22 cm

Therefore,
Circle’s perimeter

= 2 πr

= 2 \times \frac{22}{7} \times 14 = 88 cm

Area of segment = \frac{Arc length}{Perimeter of circle} \times Area of circle (π r^{2})

= \frac{22}{88} \times \frac{22}{7} \times 14 \times 14

= \frac{1}{4} \times 22 \times 2 \times 14

= 22 \times 7

= 154 sq . cm

Thus, the area of sector is

154 sq . cm

.
Correct option is 1.

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