Question

What will be the area of the circle shown if the area of the shaded part is 5 sq. cm?

A. 25 sq.cm
B. 60 sq.cm
C. 25π sq.cm
D. 150 sq.cm

( WITH EXPLANANTION )
​

Answer 1

Answer:

B. 60 sq.cm

Step-by-step explanation:

Answer 2

Answer: (B) 60 sq. cm

Concept : Circles

Given : Area of shaded region is 5 sq. cm, ∠OBA = 75°

To Find : Area of the circle

Step-by-step explanation:

∠OBA = 75°

OA and OB is the radius.

If we draw a perpendicular from center O on chord AB, then the chord will be bisected.

∠OBA = ∠OAB = 75°

∴ ∠AOB = 180° - 75° - 75° = 30°

We know that, area of a sector = $\frac{theta}{360} * \pi (radius)^{2}$

⇒ $5 = \frac{30}{360} * \pi * (radius)^{2}$

∴ $(radius)^{2} = \frac{60}{\pi }$

∴ Area of circle = $\pi (radius)^{2}$

                         = $\pi * \frac{60}{\pi }$

                          = 60 sq. cm

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