Question 17

The volume of the second cylinder is 8V.

To find the volume of the second cylinder, we use the formula for the volume of a cylinder, V = πr²h. The second cylinder has a radius of 2r and a height of 2h, leading to a calculated volume of V' = π(2r)²(2h) = π(4r²)(2h) = 8πr²h, which is 8 times the volume of the first cylinder, V.

A) 2V

This option suggests that the volume of the second cylinder is twice that of the first. However, calculating the volume shows that the second cylinder has a radius and height that increase by a factor of 2, resulting in a volume that is much larger than 2V.

B) 4V

While this option indicates a volume four times that of the first cylinder, it fails to account for the combined effect of both the radius and height doubling. The volume actually increases by a factor of 8, not 4, making this option incorrect.

C) 6V

This choice implies that the volume of the second cylinder is six times that of the first. This is inaccurate since the increase in both dimensions leads to a volume that is eight times greater, not six, therefore this option is incorrect.

D) 8V

This is the correct answer. The volume of the second cylinder, calculated based on its dimensions, results in a total volume of 8V, confirming that it is indeed eight times the volume of the first cylinder.

E) 16V

This option suggests that the second cylinder has a volume sixteen times greater than the first. However, since the calculations illustrate that the volume is actually 8V, this option is incorrect as it overestimates the volume.

Conclusion

The correct volume of the second cylinder is 8V, as derived from the formula for the volume of a cylinder. All other options incorrectly calculate the volume by underestimating or overestimating the effects of the increased dimensions, highlighting the importance of accurately applying mathematical principles in geometric calculations.