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 .
There are no choices. :/

Answer 1

At first, I thought this was going to be a dog of a bear of a problem,
but then I fixated it with my steely burning gaze and it fell apart for me.

The volume of a pyramid is   (1/3) (base area) (height)

Each of these pyramids has the same base area and the
same height, so ...

      Volume of the lower pyramid = (1/3) (base area) (height)
      Volume of the upper pyramid = (1/3) (base area) (height)

Combined volume of both pyramids = (2/3) (base area) (height) .

Now, how do the pyramids relate to the rectangular prism ?

Their base area is  (length x width) of the prism, and
their height is  (1/2 the height) of the prism.

From here, we'll work with the dimensions of the prism ... L, W, and H .

Combined volume of the pyramids = (2/3) (L x W) (1/2 H)

                                                           =  (1/3) (L x W x H) .

Volume of the prism  =  (L x W x H)

The pyramids occupy 1/3 the volume of the prism.

The ratio is  1/3 .