AD is the diameter of a circle with area 707 m2and AB = BC = CD as shown in the figure above. All curves inside the circles are semicircles with their diameters on AD. What is the cost of leveling the shaded region at the rate of Rs 63 per square meter?a)Rs 29,700b)Rs 22,400c)Rs 14,847d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?

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AD is the diameter of a circle with area 707 m² and AB = BC = CD as shown in the figure above. All curves inside the circles are semicircles with their diameters on AD. What is the cost of leveling the shaded region at the rate of Rs 63 per square meter?

a)
Rs 29,700
b)
Rs 22,400
c)
Rs 14,847
d)
None of the above

Correct answer is option 'C'. Can you explain this answer?

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CDS II - Mathematics Previous Year Question Paper 2016

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AD is the diameter of a circle with area 707 m2and AB = BC = CD as sho...

Let the diameter of the circle be d
AB = BC = CD = d/3

Area of shaded region = 2 × (Area of semicircle with diameter AC - Area of semicircle with diameter AB)

⇒ 2 × ½ × [π(d/3)² - π(d/6)²] [∵ Area of the circle = ½ × πr²]
⇒ πd²/12 = 1/3 × (πd²/4)
⇒ 1/3 × Area of the circle = 1/3 × 707
∴ Cost of leveling = 63 × 707/3 = Rs. 14, 847

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AD is the diameter of a circle with area 707 m2and AB = BC = CD as shown in the figure above. All curves inside the circles are semicircles with their diameters on AD. What is the cost of leveling the shaded region at the rate of Rs 63 per square meter?a)Rs 29,700b)Rs 22,400c)Rs 14,847d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?

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