Wooden prism

Find the mass of a regular triangular prism made of oak, whose height equals the perimeter of its equilateral triangular base, and whose base is inscribed in a circle with radius 6.M cm (where M is the month of your birth). The density of oak is 680 kg/m³.

Final Answer:

m =  1.3196 kg

Step-by-step explanation:

$$\begin{gathered} \rho =680{\text{kg/m}}^3 \\ r=6.6\text{cm}\to \text{m}=6.6:100\text{m}=0.066\text{m} \\ a=\sqrt{3}\cdot r=\sqrt{3}\cdot 0.066\doteq 0.1143\text{m} \\ {S}_1=\sqrt{3}/4\cdot a^2=\sqrt{3}/4\cdot 0.1143^2\doteq 0.0057{\text{m}}^2 \\ h=3\cdot a=3\cdot 0.1143\doteq 0.3429\text{m} \\ V=S_1\cdot h=0.0057\cdot 0.3429\doteq 0.0019{\text{m}}^3 \\ m=\rho \cdot V=680\cdot 0.0019=1.3196\text{kg} \end{gathered}$$

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