[填空题]
A plastic toy is in the shape of a right pyr 4 ,.fcxf8+ikhors7 ezvo+kj. d.garm)gx1b g(vk48* k;nxufamid. The pyramid has a square base with the sides 4 cm long. The diagram below represents this pyramid, labelled VABCD. V is the vertex of the pyramid. O is the center of the base ABCD. M is the )1mk(v*xg..vr +g b4k8jan xfkgu;odmidpoint of BC. The angle $\mathrm{V}\hat{\mathrm{B}}\mathrm{C}$ is equal to$75^{circ}C$.
1.Calculate the length of VM. cm
2.Calculate the height of the pyramid, VO. cm
3.Find the volume of the pyramid, in $cm^3$. Give your answer correct to one decimal place. $cm^3$
4.Write down your answer to part (c) in the form $a \times 10^k$, where $1 \leq a \leq 10$ and $k \in \mathbb Z$. $\times10^1\:cm^3$
Another plastic toy is in the shape of a right cone. The height of the cone is equal to the height of the pyramid, and the diameter of the cone's base is equal to 4 cm.
5.Determine whether the amount of plastic used to manufacture the pyramid is also enough to manufacture this cone. $cm^3$
After heating, the pyramid deforms in such a way that the angle $\mathrm{V}\hat{\mathrm{B}}\mathrm{C}$ decreases by 20%. The side VC decreases in length during this deformation, however sides VB and BC stay the same length.
6.Calculate
1.The new distance from the pyramid vertex V to point M. cm
2.The new area of the pyramid's side VBC. $cm^2$
