Bunuel wrote:

In the figure above, ABCD is a rectangle and the curved path is made up of 16 semicircles of equal diameter. If the total length of the curved path is 32π, then the area of rectangle ABCD is

(A) 24

(B) 32

(C) 48

(D) 64

(E) 192

Attachment:

2017-11-30_0948.png

Since the curved path is made up of 16 semicircles, each semicircular arc is 32π/16 = 2π. Thus, the diameter of each semicircle is 4 (notice that ½ x 4π = 2π). Since the length of the rectangle is made up of 6 diameters, the length = 24, and, since the width is made up of 2 diameters, the width = 8, so the area is 24 x 8 = 192.

Answer: E

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