Given the volume of the square pyramid:
[tex]V=972in^3[/tex]
You can identify that its height is represented as:
[tex]h=\frac{1}{2}x[/tex]
And "x" represents the side length of the base.
The volume of a square pyramid can be calculated using this formula:
[tex]V=\frac{a^2h}{3}[/tex]
Knowing that:
[tex]a=x[/tex]
You can set up this equation in order to find its value:
[tex]972=\frac{(x^2)(\frac{1}{2}x)}{3}[/tex]
In order to solve for "x", you need to:
1. Multiply both sides of the equation by 3:
[tex]\begin{gathered} 972\cdot3=\frac{(x^2)(\frac{1}{2}x)}{3}\cdot3 \\ \\ 2916=(x^2)(\frac{1}{2}x) \end{gathered}[/tex]
2. Multiply the variables on the right side:
[tex]2916=\frac{1}{2}x^3[/tex]
3. Multiply both sides of the equation by 2:
[tex]\begin{gathered} (2)(2916)=(\frac{1}{2}x^3)(2) \\ \\ 5832=x^3 \end{gathered}[/tex]
4. Take the cube root of both sides:
[tex]\begin{gathered} \sqrt[3]{5832}=\sqrt[3]{x^3} \\ \\ x=18 \end{gathered}[/tex]
Knowing the value of "x", you get that:
[tex]h=\frac{1}{2}(18)=9[/tex]
Hence, the answer is: The side length of the square base is 18 inches and the height of the pyramid is 9 inches.
