Tetrahedral prism

The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge if you know that the prism volume is 2187 cm³.

Final Answer:

a =  9 cm

Step-by-step explanation:

$$\begin{gathered} V=2187{\text{cm}}^3 \\ V=a^{2}h \\ {a}^{2}3a=2187 \\ {a}^3=729 \\ a=\sqrt[3]{729}=9=9\text{cm} \\ \text{ Verifying Solution: } \\ h=3\cdot a=3\cdot 9=27\text{cm} \\ {V}_2=a\cdot a\cdot h=9\cdot 9\cdot 27=2187{\text{cm}}^3 \end{gathered}$$

Try another example