Asquare pyramid has a volume of 144in cubed. give possible dimensions of the pyramid.

( show your work. )

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