Decorative 46721

How many liters of water can fit in a decorative garden tank in the shape of a regular hexagonal pyramid with a 30 cm long base edge? The depth of the tank is 30 cm.

Correct answer:

V =  23.3827 l

Step-by-step explanation:

$$\begin{gathered} r=30\text{cm} \\ a=r=30\text{cm} \\ h=30\text{cm} \\ {s}^2=h^2+a^2 \\ s=\sqrt{h^2+a^2}=\sqrt{30^2+30^2}=30\sqrt{2}\text{cm}\doteq 42.4264\text{cm} \\ w=\sqrt{s^2-(a/2{)}^2}=\sqrt{42.4264^2-(30/2{)}^2}=15\sqrt{7}\text{cm}\doteq 39.6863\text{cm} \\ {S}_1=3\cdot \sqrt{3}/2\cdot a^2=3\cdot \sqrt{3}/2\cdot 30^2=1350\sqrt{3}{\text{cm}}^2\doteq 2338.2686{\text{cm}}^2 \\ {V}_1=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 2338.2686\cdot 30\doteq 23382.6859{\text{cm}}^3 \\ V=V_1\to \text{l}=V_1:1000\text{l}=23382.6859:1000\text{l}=23.383\text{l}=23.3827\text{l} \end{gathered}$$

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