Answer:
infinite number of solutions are possible
Step-by-step explanation:
The formula for the volume of a pyramid is (1/3)(base)(height). Since this pyramid is square, the area of the base is s^2, where s represents the length of one side of the base.
Thus, 144 in^3 = (1/3)(s^2)(h), where h is the height of the pyramid.
Let's solve for the constraints on the side length s and the height h:
Multiplying 144 in^3 = (1/3)(s^2)(h) by 3 to clear out the fractions:
432 in^3 = (s^2)(h)
There are multiple answers tot his question. Let's arbirtrarily state that the height is 10 inches. Then 432 in^3 = 10s^2 in^2, and s^2 = 43.2 (in^2).
With height 10 inches, the side length of the square bottom would be the square root of 43.2 in^2: 6.57 in.
Thus, one of many solutions would be as follows:
side length of square base: 6.57 in
height of pyramid: 10 in
