To find the radius of a cone given its volume and height, you 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 that the volume \( V \) is 261.8 cm³ and the height \( h \) is 10 cm, we can rearrange the formula to solve for \( r \):
\[ r^2 = \frac{3V}{\pi h} \] \[ r = \sqrt{\frac{3V}{\pi h}} \]
Now, substituting the values:
\[ r = \sqrt{\frac{3 \times 261.8}{\pi \times 10}} \]
Calculating the numerator:
\[ 3 \times 261.8 = 785.4 \]
Calculating the denominator:
\[ \pi \times 10 \approx 31.4159 \]
Now, calculating \( r^2 \):
\[ r^2 = \frac{785.4}{31.4159} \approx 25.0 \]
Finally, taking the square root to find \( r \):
\[ r \approx \sqrt{25.0} \approx 5.0 \text{ cm} \]
So, the approximate radius of the cone is 5 cm.