该图形由一个半圆、一个大圆和一个小圆组成。O 是半圆和大圆的圆心。X 是小圆的圆心。OP = 56 cm。 使用计算器中的 π\pi 值,求非阴影部分的周长,保留两位小数。 答:___

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完整解法

10

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

Radius of semicircle R=56R = 56 cm.
Radius of large circle r=56−14=42r = 56 - 14 = 42 cm.
The small circle spans from the centre OO to the bottom of the large circle, so its diameter is equal to the radius of the large circle, which is 4242 cm.

2. Calculate the perimeter of the unshaded small circle.

Perimeter of small circle =π×d=42π= \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 =12×π×(2×56)=56π= \frac{1}{2} \times \pi \times (2 \times 56) = 56\pi cm.
Arc of large semicircle =12×π×(2×42)=42π= \frac{1}{2} \times \pi \times (2 \times 42) = 42\pi cm.
Straight segments =14+14=28= 14 + 14 = 28 cm.
Perimeter of this region =56π+42π+28=98π+28= 56\pi + 42\pi + 28 = 98\pi + 28 cm.

4. Find the total perimeter of all unshaded parts.

Total perimeter =42π+98π+28=140π+28= 42\pi + 98\pi + 28 = 140\pi + 28
140π+28≈467.82297...≈467.82140\pi + 28 \approx 467.82297... \approx 467.82 cm

答案

467.82467.82 cm

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