Pyramid height volume

A regular four-sided pyramid has a volume of 2,160 liters and a base edge length of 12 dm. Calculate the height of the needle (sketch, calculation, answer).

Final Answer:

h =  45 dm

Step-by-step explanation:

$$\begin{gathered} a=12\text{dm} \\ V=2160\text{l}\to {\text{dm}}^3=2160\cdot 1{\text{dm}}^3=2160{\text{dm}}^3 \\ {S}_1=a^2=12^2=144{\text{dm}}^2 \\ V=\frac{1}{3}\cdot S_1\cdot h \\ h=\frac{3\cdot V}{S_1}=\frac{3\cdot 2160}{144}=45\text{dm} \end{gathered}$$

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