The arc length of a semicircle is πR,

The circumference of the bottom surface rolled into a cone is πR,

The radiu of that bottom surface is πR/2π=R/2,

The bottom area is π (r/2) 2 = π r? /4

And the bus length is r,

Therefore, the cone height is √ [r 2-(r/2) 2] = √ 3r/2.

The volume is 1/3*πR? /4*√3R/2=]=√3πR？ /24

That is, its volume is √3πR? /24

2、

Let the intersection of A'B'∥AB and A'B' be perpendicular to CD, and the intersection point is g. In the rectangle A'B'BA, AA'=BB'=√7,

AB'=A'B=2R (circumscribed circle diameter) =√43. S table =43π.

3、

The vertices of rectangular ABCD are all on the sphere with radius of 4, and AB=6, BC=2√3.

Rectangular diagonal AC = √ (AB 2+BC 2) = √ (36+12) = 4 √ 3.

The height from O center to rectangular ABCD is: h = √ (R2-(AC/2) 2) = √ (4 2-(2 √ 3) 2) = 2.

∴ The volume of pyramid O-ABCD is v =1/3 * ab * BC * h =1/3 * 6 * 2 √ 3 * 2 = 3 √ 3.