单选题
The figure at the right consists of four semicircles in a large semicircle. If the small semicircles have radii of 1, 2, 3, and 4, what is the perimeter of the shaded region?
【正确答案】
B
【答案解析】In the given figure, the diameters of the four small semicircles are 2, 4, 6, and 8, so the diameter of the large semicircle is 2 + 4 + 6 + 8 = 20, and its radius is 10. The perimeter of the shaded region is the sum of the circumferences of all five semicircles.
Since the circumference of a semicircle is π times its radius, the perimeter is π+ 2π + 3π + 4π + 10π = 20π.
Since the circumference of a semicircle is π times its radius, the perimeter is π+ 2π + 3π + 4π + 10π = 20π.