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Mridul Gupta
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Asked: 2023-02-23T08:41:40+00:00 In:

In Figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

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In Figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

Please provide me solution for this question and video explanation for better understanding.
NCERT class 10 chapter 12
Page No. 236
Exercise 12.3
Question No. 9

chapter 12class 10ncert
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      In Figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

      Radius of smaller circle = 7/2 cm
      Area of smaller circle = πr² = π(7/2)² = 22/7 × 7/2 × 7/2 = 77/2 cm²
      Radius of larger circle = 7 cm
      Area of semicircle AECFB
      = 1/2 × πr² = π(7)² = 1/2 × 22/7 7 × 7 = 77 cm²
      Area of triangle ACB
      = 1/2 × AB × OC = 1/2 × 14 × 7 = 49 cm²
      Area of Shaded Region
      = Area of smaller circle + Area of semicircle AECFB – Area of triangle ACB
      = (77/2 + 77 – 49) cm² = (38.5 + 28) cm² = 66.5 cm²

      Here you can see the video explanation of this question for better understanding😄👇

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