Sandpile

Sand was piled into an approximately conical shape. Workers wanted to determine the volume (amount of sand) and measured the circumference of the base and the total length of both slant sides of the cone.

What is the volume of the sand cone if the circumference of the base is 25 m and the sum of the two slant sides is 10 m?

Final Answer:

V =  50.2 m³

Step-by-step explanation:

$$\begin{gathered} o=25\text{m} \\ c=10\text{m} \\ o=2\pi \cdot r \\ r=\frac{o}{2\pi }=\frac{25}{2\cdot 3.1416}\doteq 3.9789\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3.9789^2\doteq 49.7359\text{m} \\ 2s=c \\ s=c/2=10/2=5\text{m} \\ {s}^2=h^2+r^2 \\ h=\sqrt{s^2-r^2}=\sqrt{5^2-3.9789^2}\doteq 3.028\text{m} \\ V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 49.7359\cdot 3.028=50.2{\text{m}}^3 \end{gathered}$$

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