4 mm\n8 mm\nwhat is the ratio of the volume of the smaller triangular pyramid to the volume\nthe larger…

Explanation:

Step1: Recall Volume of Pyramid Formula

The volume ( V ) of a pyramid is given by ( V = \frac{1}{3}Bh ), where ( B ) is the area of the base and ( h ) is the height. For similar pyramids, the ratio of their volumes is the cube of the ratio of their corresponding linear dimensions (like height, base edge, etc.).

Step2: Find the Ratio of Corresponding Heights

The height of the smaller pyramid is ( 4 , \text{mm} ) and the height of the larger pyramid is ( 8 , \text{mm} ). The ratio of the heights (smaller to larger) is ( \frac{4}{8} = \frac{1}{2} ).

Step3: Calculate the Ratio of Volumes

Since the volumes of similar solids are in the ratio of the cubes of their corresponding linear measurements, the ratio of the volume of the smaller pyramid to the larger pyramid is ( \left( \frac{1}{2} \right)^3 = \frac{1^3}{2^3} = \frac{1}{8} ).

Answer:

( 1:8 )