Sandpile

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

What is the volume of the sand cone, if the circumference of the base is 6 m and length of the two sides together 6 m?

Correct result:

volume is:  2.7 m3

Solution:

r=62π=0.95 m V=13Sv=13πr2624r2=2.7 m3 r = \dfrac{ 6}{2\pi} = 0.95 \ m \ \\ V = \dfrac{1}{3}\cdot S \cdot v = \dfrac{1}{3}\cdot \pi r^2 \cdot \sqrt{\dfrac{ 6^2}{4}- r^2} = 2.7 \ \text{m}^3



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