OABC is a quadrant of a circle of radius 7 cm. If OD = 4 cm, find the area of the shaded region. [Use π= 22 7 ]

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OABC is a quadrant of a circle of radius 7 cm. If OD = 4 cm, find the area of the shaded region. [Use $π = 227$ ]

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47.69

c m 2

78.9

c m 2

24.5

c m 2

45.8

c m 2

answer is C.

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Detailed Solution

Given that the radius of the circle is 7 cm.
We have to find the area of the shaded region.
Question Image

The area of a quadrant can be expressed as

A = 14 π r 2

.
From the figure,

OC=radius of the circle ⇒ OC= 7 c m

Thus, the area of the shaded region,

A s

is,

A s = area of quadrant - area of ODC ⇒ A s = 14 π r 2 − 12 O D O C ⇒ A s = 14 π 72 − 1247 ⇒ A s = 38.5 − 14 ⇒ A s = 24.5 cm 2

The area of the shaded region is 24.5

c m 2

.
Therefore, the correct option is 3.

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