Answer:
The height of the pyramid is 6 cm.
Step-by-step explanation:
The volume of a square pyramid is given by:
[tex] V = \frac{1}{3}A_{b}h = 72 cm^{3} [/tex]
Where:
[tex]A_{b}[/tex]: is the area of the base
h: is the height
Since the base edge length is equal to the height, the area of the base is:
[tex]A_{b} = l^{2} = h^{2} [/tex]
Hence, the height is:
[tex] 72 cm^{3} = \frac{1}{3}A_{b}h = \frac{1}{3}h^{2}h [/tex]
[tex] h = (3*72 cm^{3})^{1/3} = 6 cm [/tex]
Therefore, the height of the pyramid is 6 cm.
I hope it helps you!
