Given that a triangle pyramid has a base area of 72 cm squared and a height/altitude of 9 cm.
A cross-section is cut 3 cm from the base of the pyramid.
So, the dilating factor is
[tex]\frac{1}{3}[/tex]
Now, the base area of the triangle pyramid is 72 square sm.
So, the area of the cross-section is
[tex]\begin{gathered} A=(\frac{1}{3})^2\times72 \\ =\frac{1}{9}\times72 \\ =8 \end{gathered}[/tex]
So, the area of the cross-section is 8 square cm
Now, the given height of the pyramid is 9 cm.
So, the volume of the entire pyramid is
[tex]\begin{gathered} V=\frac{1}{3}Ah \\ =\frac{1}{3}\times72\times9 \\ =216 \end{gathered}[/tex]
Hence, the volume of the entire pyramid is 216 cubic centimeters.
