Answer:
64:343
Explanation:
The ratio of the volume of the small pyramid to the volume of the large pyramid is equal to the cube of the ratio of their corresponding linear dimensions.
In this case, the ratio of the heights is 4/7, so the ratio of the volumes is (4/7)^3 = 64/343.
Therefore, the ratio of the volumes of the two pyramids is 64:343.
Here is a more detailed explanation:
The volume of a pyramid is given by the formula:
V = ⅓*Bh
where V is the volume, B is the area of the base, and h is the height.
Since the two pyramids are similar, the ratio of their areas is equal to the square of the ratio of their corresponding ki linear dimensions.
In this case, the ratio of the heights is 4/7, so the ratio of the areas is (4/7)^2 = 16/49.
Therefore, the ratio of the volumes of the two pyramids is:
(1/3) * (16/49) * (4/7) = 64/343