Mathematics

In the figure (ii) given below, there are five squares each of side 2 cm.
(i) Find the radius of the circle.
(ii) Find the area of the shaded region. (Take π = 3.14).

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(i) Let O be the center of the circle.

B be the mid-point of side of square.

From figure,

OB = 2 + 1 = 3 cm

AB = 1 cm

Using Pythagoras theorem,

OA = $\sqrt{OB^2 + AB^2}$

OA = $\sqrt{3^2 + 1^2} = \sqrt{9 + 1} = \sqrt{10}$ .

So, the radius of the circle = $\sqrt{10}$ cm.

Hence, the radius of circle = $\sqrt{10}$ cm.

(ii) We know that,

Area of the circle = πr².

= 3.14 × $\sqrt{10}^2$

= 3.14 × 10

= 31.4 cm².

Area of 5 square of side 2 cm each = 2² × 5

= 4 × 5

= 20 cm².

So, the area of shaded portion = 31.4 – 20 = 11.4 cm².

Hence, area of shaded portion = 11.4 cm².

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