Answer:
8 cubic millimeters
Explanation:
The larger pyramid has a height of 8 and the smaller pyramid has a height of 4
Therefore the scale factor from smaller to larger = 8/4 = 2
This means each side of the base of the square pyramid is also twice the length of each side of the smaller pyramid
Let the base side length of the smaller pyramid be a and height h
The volume of a square pyramid with side a and height h is given by the formula
V = (1/3) a² h
So volume of smaller pyramid
V₂ = (1/3) a² h
If the pyramid is scaled by a factor of 2, then the larger pyramid will have each side = 2a and height = 2h
Therefore the volume of the larger pyramid in terms of a and h will be
V = (1/3) (2a)² (2h)
(2a)² = 4a²
So
V₁ = (1/3) (4a²) (2h)
V₁ = (1/3) a² h · 8
V₁ = 8 · (1/3) a² h = 8 · V₂
So the larger pyramid volume is 8 times the smaller pyramid
Smaller pyramid volume is given as 1 cubic millimeter
Larger pyramid volume = 8 x 1 = 8 cubic millimeters