Question

Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the prism, expressed as a fraction in simplest form, is
.

Answer 1

Check the picture below.

now, bear in mind that, the volume of a pyramid is (1/3)Bh, in this case, their height is half of "h", or half of that of the rectangular prism.

anyhow, the combined volume is 2 times that much, let's check their ratio.

$\bf \cfrac{\textit{volume of two pyramids}}{\textit{volume of prism}}\qquad \cfrac{2\left( \frac{1}{3}B\cdot \frac{h}{2} \right)}{Bh}\implies \cfrac{\frac{2Bh}{6}}{Bh}\implies \cfrac{\frac{Bh}{3}}{Bh} \\\\\\ \cfrac{\frac{Bh}{3}}{\frac{Bh}{1}}\implies \cfrac{Bh}{3}\cdot \cfrac{1}{Bh}\implies \cfrac{1}{3}$