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?

Formula Used:

Area of Circle = πr2 ,r= radius

Area of semicircle = \(\frac{1}{2}\)πr2

Calculation:

Let the diameter of the circle be d

It is given that AB = BC = CD 

Let AB = BC = CD = d/3

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

Using above formula

= 2 × ½ × [π(d/3)² - π(d/6)²]              

= πd²/12

= 1/3 × (πd²/4)

= 1/3 × Area of the circle = 1/3 × 707

Cost of leveling = Area of shaded region × Rate of levelling

Cost of leveling = 707/3 × 63 = Rs. 14, 847

∴ Correct option is Rs 14,847