To find the radius of the cone, we can use the volume formula for a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
Given that the volume \( V \) is 500 cm³ and the height \( h \) is approximately 13.5 cm, we can plug in these values and solve for the radius \( r \).
\[ 500 = \frac{1}{3} \pi r^2 (13.5) \]
Multiply both sides by 3 to eliminate the fraction:
\[ 1500 = \pi r^2 (13.5) \]
Now, divide both sides by \( \pi \times 13.5 \):
\[ r^2 = \frac{1500}{\pi \times 13.5} \]
Calculating the denominator:
\[ \pi \approx 3.14 \quad \Rightarrow \quad \pi \times 13.5 \approx 3.14 \times 13.5 \approx 42.39 \]
Now we can substitute this value back in:
\[ r^2 \approx \frac{1500}{42.39} \approx 35.39 \]
Now, take the square root to solve for \( r \):
\[ r \approx \sqrt{35.39} \approx 5.95 \text{ cm} \]
Rounding gives us approximately 6 cm.
Therefore, the approximate radius of the cone is 6 cm.
The correct response is 6 cm.