A first circular cylinder has radius r and height h, with volume V = πr²h. A second cylinder has radius 2r and height 2h. Express its volume in terms of V.

This choice suggests that the volume of the second cylinder is only double that of the first. However, given that both the radius and height are doubled, the volume increases more significantly than just a factor of two. This option underestimates the effect of the changes in both dimensions.

Choosing 4V implies that the volume quadruples, which would be the case if only one of the dimensions (either radius or height) were doubled. Since both dimensions are doubled, the volume increases by a factor of eight, making this option incorrect.

This option indicates a volume that is not a direct factor of the original volume based on the doubling of both dimensions. The calculation for the new volume shows that it is not a simple multiplication of the original volume, and thus 6V does not represent the correct scaling.

This choice suggests a volume that is excessively high, implying that the doubling of both dimensions results in an even larger factor of increase. However, the calculation reveals that the volume doubles in each dimension, leading to an overall factor of eight, making this answer incorrect.