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SSC CGL 2024 PYQ — Question 51

SSC CGL - 09 Sep 2024 - Shift 3 • Quantitative Aptitude • Q51

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Find the area (in cm2) of the sector whose perimeter is 64364\over3 cm and central angle is 60°. (Use π = 22722\over7.)

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Correct answer: B

Explanation

The correct answer is Option 2 i.e. 77377\over3.

We know that,

Area of the sector = θ/360 × πr2

Arc length = θ/360 × 2πr

Arc length = 60/360 × 2 × 22/7 × r

⇒ 1/6 × 2 × 22/7 × r

⇒ 22r/21

Given that the perimeter of the sector = 64/3

⇒ 64/3 = r + r + 22r/21

⇒ 64/3 = 2r + 22r/21

⇒ 64/3 = (42r + 22r)/21

⇒ 64/3 = 64r/21

⇒ r = 21/3

⇒ r = 7

Now,

Area of the sector = θ/360 × πr2

⇒ 60/360 × 22/7 × 7 × 7

⇒ 1/6 × 22 × 7 = 77/3