1.97: 3D angles in a pyramid

Figure 2 shows a solid $VABCDEFGH$ which is formed by joining a cuboid $ABCDEFGH$ to a right pyramid $VABCD$. The height of the cuboid and the height of the pyramid are both $h$ cm and $FG=8$ cm and $GH=6$ cm. The total volume of the solid is $256\text{ cm}^3$.

(a) Show that $h=4$. (2)

(b) Find, in cm to 3 significant figures, the length of $VF$. (3)

Find, to the nearest $0.1^\circ$,

(c) the angle between $VA$ and the plane $ABCD$, (3)

(d) the acute angle between the plane $VAB$ and the plane $ABHE$. (4)