Answer:
Only the second and third statements are correct:
Doubling r quadruples the volume.
Doubling h doubles the volume.
Step-by-step explanation:
The volume of a cylinder is given by:
[tex]\displaystyle V=\pi r^2h[/tex]
We can go through each statement and examine its validity.
Statement 1)
If the radius is doubled, our new radius is now 2r. Hence, our volume is:
[tex]\displaystyle V=\pi (2r)^2h=4\pi r^2h[/tex]
So, compared to the old volume, the new volume is quadrupled the original volume.
Statement 1 is not correct.
Statement 2)
Using the previous reasonsing, Statement 2 is correct.
Statement 3)
If the height is doubled, our new height is now 2h. Hence, our volume is:
[tex]V=\pi r^2(2h)=2\pi r^2h[/tex]
So, compared to the old volume, the new volume has been doubled.
Statement 3 is correct.
Statement 4)
Statement 4 is not correct using the previous reasonsing.
Statement 5)
Doubling the radius results in 2r and doubling the height results in 2h. Hence, the new volume is:
[tex]V=\pi (2r)^2(2h)=\pi (4r^2)(2h)=8\pi r^2h[/tex]
So, compared to the old volume, the new volume is increased by eight-fold.
Statement 5 is not correct.
