A circular cylinder has radius r and height h. A second cylinder has radius 2r and height 2h. What is the volume of the second cylinder in terms of V = πr²h?

This choice suggests that the volume of the second cylinder is half of what it actually is. The calculation of volume depends on both the square of the radius and the height; hence, this choice significantly underestimates the increase in volume due to the doubled dimensions.

While this option reflects an increase in volume, it is based on the incorrect assumption that only the radius contributes to volume scaling. The height was also doubled, meaning the volume increases by a factor of 8, not 4.

This choice incorrectly estimates the volume by suggesting an arbitrary increase. The volume scaling follows a clear geometric principle where both radius and height are doubled, leading to a multiplication of the original volume by 8, not 6.

This option overestimates the volume by assuming both dimensions contribute to a multiplication of the original volume by 16. This misunderstanding neglects the proper geometric relationship between the dimensions in volume calculation, which only doubles both radius and height.