The side length of the square base is 18 inches and the height of the pyramid is 9 inches.
Step-by-step explanation:
Step 1:
The volume of a square pyramid is calculated by multiplying the square of the base edge with the height of the pyramid and [tex]\frac{1}{3}[/tex].
The volume of a square pyramid, [tex]V = a^{2} \frac{h}{3}.[/tex]
Step 2:
From the given diagram, the base edge is the length of the four base edges which is x inches in this pyramid. a = x inches.
The height of the pyramid is from the base to the top, h = [tex]\frac{x}{2}[/tex] inches .
The volume of a square pyramid, [tex]V = 972.[/tex]
Substituting the known values, we get
[tex]972 = (x)^{2} (\frac{x}{2}) (\frac{1}{3} ) = \frac{x^{3} }{6} .[/tex]
[tex]x^{3} = 6(972) = 5,832. x = \sqrt[3]{5,832} = 18.[/tex]
So x is 18 inches long.
The side length [tex]= x = 18[/tex] inches.
The height of the pyramid [tex]= \frac{x}{2} = \frac{18}{2} = 9[/tex] inches.
