Sandpile

Auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the volume (amount of sand) and, therefore, measure the base's circumference and the length of both sides of the cone (over the top).

What is the sand cone's volume if the circumference of the base is 25 m and the length of the two sides together 10 m?

Correct 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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