Equilateral shell

The glass weight has the shape of a regular four-sided pyramid with a base edge of 10 cm. The shell walls are equilateral triangles. What is the weight in grams of the paperweight if the density of the glass is 2500 kg/m³?

Final Answer:

m =  589.2557 g

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ \rho =2500{\text{kg/m}}^3\to {\text{g/cm}}^3=2500:1000{\text{g/cm}}^3=2.5{\text{g/cm}}^3 \\ {S}_1=a^2=10^2=100{\text{cm}}^2 \\ {h}_2=\sqrt{3}\cdot a/2=\sqrt{3}\cdot 10/2=5\sqrt{3}\text{cm}\doteq 8.6603\text{cm} \\ h=\sqrt{h_2^2-(a/2{)}^2}=\sqrt{8.6603^2-(10/2{)}^2}=5\sqrt{2}\text{cm}\doteq 7.0711\text{cm} \\ V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 100\cdot 7.0711\doteq 235.7023{\text{cm}}^3 \\ m=\rho \cdot V=2.5\cdot 235.7023=589.2557\text{g} \end{gathered}$$

Try another example