Final answer:
To determine the dimensions of the rectangular solid, use the formula for volume and find the values of l and h that satisfy the equation.
Step-by-step explanation:
To determine the dimensions of the rectangular solid, we need to use the formula for the volume of a rectangular solid: V = l x w x h. We know that the volume is 8000 cubic inches. Let's assume that the base of the rectangular solid is a square, so we can let l = w. Substituting these values into the formula, we get:
8000 = l^2 x h
Now, we need to find the values of l and h that satisfy this equation. We can start by finding the prime factorization of 8000, which is 2^6 x 5^3. So, we can express the volume as 2^6 x 5^3 = l^2 x h.
Here are a few possible pairs of l and h that satisfy the equation:
- l = 2^3 x 5 = 40, h = 2^3 x 5^2 = 200
- l = 2^2 x 5^2 = 100, h = 2^4 x 5 = 80
- l = 2^3 x 5^2 = 200, h = 2^2 x 5 = 20
So, there are multiple sets of dimensions that yield a volume of 8000 cubic inches for a rectangular solid with a square base.