F4 Maths 3-D problems ( -.- )

Fig. I shows a triangular sheet of paper ABC which is cut along the
diagonal of a square sheet of paper of side 10 cm. O is the mid - point BC.

a) Find OB, OC and OA in surd form.

b) In figure II, the triangular sheet of paper is folded up along along OA
such that AB and AC lie on a horizontal plane. Suppose angle
BAC = 40 degree and P is the projection of O on the horizontal plane.

i) Find BC.

ii) Find angle BOC.

iii) FInd the volume of OABC. (HInt: Volume of pyramid = 1/3 x base
area x height)

iv) Hence, find OP.

Figure: http://img532.imageshack.us/img532/5947/43mathso.jpg