The arc length of a semicircle is π/2.

Take the semicircle as the side of the conical Christmas hat, and the small circle can just be used as the bottom.

∴ Let the radius of the small circle be r, then: 2πr=πa/2.

Solution: r=a/4

As shown in the figure, the center of the small circle is B, the center of the semicircle is C, and BA⊥CA is at point A,

Then: AC? +AB？ =BC？

Namely: (a/4)? +(b/2)？ =(3a/4)？ Ordered: b=av2

So choose D.