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.

Correct answer:

V =  31.1032 m³
m =  19906.069 kg

Step-by-step explanation:

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

$$\begin{gathered} q=640 \\ m=q\cdot V=640\cdot 31.1032=19906.069\text{kg} \end{gathered}$$

Try another example