a)
Check the picture below.
b)
volume wise, we know the smaller pyramid is 1/8 th of the whole pyramid, so the volume of the whole pyramid must be 8/8 th.
Now, if we take off 1/8 th of the volume of whole pyramid, what the whole pyramid is left with is 7/8 th of its total volume, and that 7/8 th is the truncated part, because the 1/8 we chopped off from it, is the volume of the tiny pyramid atop.
Now, what's the ratio of the tiny pyramid to the truncated bottom?
[tex]\stackrel{\textit{\Large Volumes}}{\cfrac{\textit{small pyramid}}{\textit{frustum}}\implies \cfrac{~~\frac{1}{8}whole ~~}{\frac{7}{8}whole}}\implies \cfrac{~~\frac{1}{8} ~~}{\frac{7}{8}}\implies \cfrac{1}{8}\cdot \cfrac{8}{7}\implies \cfrac{1}{7}[/tex]
