Question

In the following figure, AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.​

Answer 1

Answer:

The area of shaded region is 115.5 cm² .

Step-by-step explanation:

Given :  

AB & CD are two diameters of a bigger circle & OD is the diameter of a smaller circle.

OA = 7 cm

Radius of a bigger circle,R = OA = 7 cm

Radius of smaller circle, r = OA/2 = 7/2 = 3.5 cm

 

Area of bigger circle ,A1 = πR²

A1 = 22/7 × 7 × 7  

A1 = 22 × 7  

A1 = 154 cm²

Area of bigger circle = 154 cm²

 

Area of smaller, A2  = πr²

A2 = 22/7 × 3.5 × 3.5

A2 = 22 × 0.5 × 3.5

A2 = 11 × 3.5

A2 = 38.5 cm²

Area of smaller = 38.5 cm²

 

Area of shaded region ,A = Area of bigger circle ,A1 - Area of smaller, A2

A = A1 - A2

A = 154 - 38.5  

A = 115.5 cm²

Area of shaded region = 115.5 cm²

Hence, the area of shaded region is 115.5 cm² .

HOPE THIS ANSWER WILL HELP YOU….

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Answer 2

Answer:

Area of the shaded region (A) = 115.5cm²

Step-by-step explanation:

i ) Radius of the big circle (R) = 7cm

Radius of the small circle(r) = R/2 cm

Now ,

Area of the shaded region (A)

= Area of the big circle - area of the

small circle

= πR² - πr²

= πR² - π(R/2)²

= πR² - πR²/4

= (4πR²-πR²)/4

= (3πR²)/4

= (3×22×7×7)/(7×4)

= 115.5 cm²

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