In figure, circle $O$ has diameter $¯ ¯¯¯¯¯¯ ¯ A B$ of the length $8$ . If smaller circle $P$ is tangent to diameter $¯ ¯¯¯¯¯¯ ¯ A B$ at point $O$ and is also tangent to circle $O$ , calculate the approximate area of the shaded region.

3.14

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6.28

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9.42

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12.57

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25.13

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Solution

The correct option is C $6.28$
Given, $A B = 8$
$∴ O B = \frac{8}{2} = 4$
Area of semicircle $A O B$ is $\frac{1}{2} \times \frac{22}{7} \times 4^{2} = \frac{22 \times 8}{7} = 25.14$
$\Rightarrow O P = \frac{O B}{2} = 2$
Area of smaller circle is $\frac{22}{7} \times 2^{2} = \frac{22 \times 4}{7} = 12.57$
Area of shade region is $\frac{(25.14 - 12.57)}{2} = \frac{12.57}{2} = 6.28$

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In figure, circle O has diameter ¯¯¯¯¯¯¯¯AB of the length 8. If smaller circle P is tangent to diameter ¯¯¯¯¯¯¯¯AB at point O and is also tangent to circle O, calculate the approximate area of the shaded region.

The correct option is C 6.28Given, AB=8 ∴OB=82=4Area of semicircle AOB is 12×227×42=22×87=25.14⇒OP=OB2=2Area of smaller circle is 227×22=22×47=12.57Area of shade region is (25.14−12.57)2=12.572=6.28

In figure, circle $O$ has diameter $¯ ¯¯¯¯¯¯ ¯ A B$ of the length $8$ . If smaller circle $P$ is tangent to diameter $¯ ¯¯¯¯¯¯ ¯ A B$ at point $O$ and is also tangent to circle $O$ , calculate the approximate area of the shaded region.