To find the radius of a cone given its volume, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
We know the volume \( V = 6,443.28 \) cubic meters. However, we also need the height \( h \) to find the radius \( r \). If we don't have the height, we cannot uniquely determine the radius from the volume alone without making assumptions about the height.
If we assume that the height is given or that we have some particular height in mind, we can proceed. For now, let's express \( r \) in terms of \( h \):
Rearranging the formula to solve for \( r \):
\[ r^2 = \frac{3V}{\pi h} \]
\[ r = \sqrt{\frac{3V}{\pi h}} \]
Substituting in \( V = 6,443.28 \) and using \( \pi \approx 3.14 \):
\[ r = \sqrt{\frac{3 \times 6443.28}{3.14 h}} = \sqrt{\frac{19329.84}{3.14 h}} = \sqrt{\frac{6153.06}{h}} \]
Without the height \( h \), we cannot compute a specific value for \( r \). If you have a specific height for the cone, please provide that, and we will calculate \( r \). Otherwise, you'll need that information to find a unique solution for the radius.
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