Explanation:

To determine how the volume changes when both the height and radius of a cone are doubled, let’s break it down:

- The volume \( V \) of a cone is given by the formula:

$$ V = \frac{1}{3} \pi r^2 h $$

where \( r \) is the radius, and \( h \) is the height.

- Doubling the radius (\(2r\)) results in the new volume expression:

$$ V_{\text{new}} = \frac{1}{3} \pi (2r)^2 h = \frac{1}{3} \pi \times 4r^2 \times h $$

- Doubling the height (\(2h\)) results in the final new volume as:

$$ V_{\text{new}} = \frac{1}{3} \pi \times 4r^2 \times 2h = 8 \times \left(\frac{1}{3} \pi r^2 h\right) $$

- Therefore, the new volume is 8 times the original volume.

- Thus, the correct answer is: Option 2: 8 times