Gravel - cone

The mound of gravel has a regular circular cone shape with a height of 3.3 meters and a base circumference of 18.85 meters. How many cubic meters of gravel are in a pile? Calculate the weight of gravel if its density is p = 640 kg/cubic m.

Final Answer:

V =  31.1032 m³
m =  19906.069 kg

Step-by-step explanation:

$$\begin{gathered} h=3.3\text{m} \\ o=18.85\text{m} \\ r=\frac{o}{2\pi }=\frac{18.85}{2\cdot 3.1416}\doteq 3.0001\text{m} \\ S=\pi \cdot r^2=3.1416\cdot 3.0001^2\doteq 28.2757{\text{m}}^2 \\ V=\frac{S\cdot h}{3}=\frac{28.2757\cdot 3.3}{3}=31.1032{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} \rho =640{\text{kg/m}}^3 \\ m=\rho \cdot V=640\cdot 31.1032=19906.069\text{kg} \end{gathered}$$

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