To find the radius of the cone, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given:
- \( V = 261.8 , \text{cm}^3 \)
- \( h = 10 , \text{cm} \)
We can rearrange the formula to solve for \( r^2 \):
\[ r^2 = \frac{3V}{\pi h} \]
Now, substituting the given values:
\[ r^2 = \frac{3 \times 261.8}{\pi \times 10} \]
Calculating this step by step:
- \( 3 \times 261.8 = 785.4 \)
- \( \pi \times 10 \approx 31.4 \) (using \( \pi \approx 3.14 \))
- Now calculate:
\[ r^2 \approx \frac{785.4}{31.4} \approx 25.0 \]
Now, taking the square root to find \( r \):
\[ r \approx \sqrt{25.0} \approx 5.0 , \text{cm} \]
Thus, the approximate radius of the cone is \( \text{5 cm} \).
The answer is 5 cm.
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