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, and \( h \) is the height. We know:
- \( V = 261.8 , \text{cm}^3 \)
- \( h = 10 , \text{cm} \)
We can rearrange the formula to solve for \( r \):
\[ r^2 = \frac{3V}{\pi h} \]
Substituting the values we have:
\[ r^2 = \frac{3 \times 261.8}{\pi \times 10} \]
Calculating the right side step by step:
- Calculate \( 3 \times 261.8 = 785.4 \).
- Now, we divide by \( \pi \times 10 \). Using \( \pi \approx 3.14 \):
\[ \pi \times 10 \approx 31.4 \]
- Now calculate:
\[ r^2 = \frac{785.4}{31.4} \approx 25.0 \]
- Taking the square root to find \( r \):
\[ r \approx \sqrt{25.0} = 5.0 \]
Rounding to the nearest whole number, we find:
\[ r \approx 5 , \text{cm} \]
Thus, the approximate radius of the cone is \( \textbf{5 cm} \). The correct answer is:
4. 5 cm.