A museum displays a decorative solid sculpture in the form of a right pyramid, which is precisely enclosed inside a clear rectangular glass case (a right rectangular prism). The base of the pyramid is congruent to the rectangular bottom face of the glass case, and the height of the pyramid is equal to the vertical height of the case. What is the ratio of the volume of the pyramid sculpture to the volume of the outer glass case?

The correct answer is 1 : 3.

Step 1: Understand the formulas for the volume of a prism and a pyramid
A right rectangular prism (the glass case) with length $l$, width $w$, and height $h$ has a base area of:

$B=l\times w$

The total volume of the rectangular glass case, $V_{\text{case}}$, is calculated using the formula:

$V_{\text{case}}=\text{Base Area}\times \text{Height}=B\times h$

A pyramid with the exact same base area $B$ and height $h$ has a volume, $V_{\text{pyramid}}$, given by:

$V_{\text{pyramid}}=\frac{1}{3}\times \text{Base Area}\times \text{Height}=\frac{1}{3}\times B\times h$

Step 2: Calculate the ratio of the two volumes
To find the ratio of the volume of the pyramid sculpture to the volume of the outer glass case, we divide $V_{\text{pyramid}}$ by $V_{\text{case}}$:

$\text{Ratio}=\frac{V_{\text{pyramid}}}{V_{\text{case}}}=\frac{\frac{1}{3}\times B\times h}{B\times h}$

Simplifying the expression by canceling out the common terms $B\times h$:

$\text{Ratio}=\frac{1}{3}$

Conclusion:
Expressed as a ratio, the volume of the pyramid sculpture to the volume of the outer rectangular glass case is 1 : 3.