The figure is made up of a semicircle, a large circle and a small circle. O is the centre of the semicircle and the large circle. X is the centre of the small circle. OP = 56 cm. Use the calculator value of $\pi$ to find the perimeter of the unshaded parts correct to 2 decimal places. Ans : ___

1. Find the radius of the large circle and the diameter of the small circle.

Radius of semicircle $R = 56$ cm.
Radius of large circle $r = 56 - 14 = 42$ cm.
The small circle spans from the centre $O$ to the bottom of the large circle, so its diameter is equal to the radius of the large circle, which is $42$ cm.

2. Calculate the perimeter of the unshaded small circle.

Perimeter of small circle $= \pi \times d = 42\pi$ cm.

3. Calculate the perimeter of the unshaded region inside the semicircle.

This region is bounded by the arc of the semicircle, the arc of the large semicircle, and two straight segments.
Arc of semicircle $= \frac{1}{2} \times \pi \times (2 \times 56) = 56\pi$ cm.
Arc of large semicircle $= \frac{1}{2} \times \pi \times (2 \times 42) = 42\pi$ cm.
Straight segments $= 14 + 14 = 28$ cm.
Perimeter of this region $= 56\pi + 42\pi + 28 = 98\pi + 28$ cm.

4. Find the total perimeter of all unshaded parts.

Total perimeter $= 42\pi + 98\pi + 28 = 140\pi + 28$
$140\pi + 28 \approx 467.82297... \approx 467.82$ cm