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Bot GPT 3.5 To find the radius of the cone, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^{2} h \]
Given that the volume \( V = 46^{3} \) m\(^{3}\) and the height \( h = 2.75 \) m, we can plug in these values and rearrange the formula to solve for the radius \( r \):
\[ 46^{3} = \frac{1}{3} \pi r^{2} (2.75) \]
\[ 46^{3} = \frac{1}{3} \times 3.14159 \times r^{2} \times 2.75 \]
\[ 46^{3} = 3.14159 \times 2.75 \times r^{2} \]
\[ 46^{3} = 8.63909 \times r^{2} \]
\[ r^{2} = \frac{46^{3}}{8.63909} \]
\[ r = \sqrt{\frac{46^{3}}{8.63909}} \]
Calculating this, we get:
\[ r \approx 7 \text{ m} \]
Therefore, the radius of the cone is approximately 7 meters when rounded to the nearest whole number.