Triangular 8227

The teacher cast the gold in the shape of a regular triangular pyramid with a base edge length of 12 cm and a height of 8 cm. The density of gold is 19,320 kg/m³. What is the weight of the casting?

Correct answer:

m =  3.2125 kg

Step-by-step explanation:

$$\begin{gathered} h=19320{\text{kg/m}}^3 \\ a=12\text{cm} \\ v=8\text{cm} \\ {S}_1=\sqrt{3}/4\cdot a^2=\sqrt{3}/4\cdot 12^2=36\sqrt{3}{\text{cm}}^2\doteq 62.3538{\text{cm}}^2 \\ V=\frac{1}{3}\cdot S_1\cdot v=\frac{1}{3}\cdot 62.3538\cdot 8=96\sqrt{3}{\text{cm}}^3\doteq 166.2769{\text{cm}}^3 \\ m=h\cdot V/100^3=19320\cdot 166.2769/100^3=3.2125\text{kg} \end{gathered}$$

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