Answer:
Only the second and third statements are correct:
Doubling <em>r</em> quadruples the volume.
Doubling <em>h</em> doubles the volume.
Step-by-step explanation:
The volume of a cylinder is given by:
![\displaystyle V=\pi r^2h](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%20r%5E2h)
We can go through each statement and examine its validity.
Statement 1)
If the radius is doubled, our new radius is now 2<em>r</em>. Hence, our volume is:
![\displaystyle V=\pi (2r)^2h=4\pi r^2h](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%20%282r%29%5E2h%3D4%5Cpi%20r%5E2h)
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 2<em>h</em>. Hence, our volume is:
![V=\pi r^2(2h)=2\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2%282h%29%3D2%5Cpi%20r%5E2h)
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 2<em>r</em> and doubling the height results in 2<em>h</em>. Hence, the new volume is:
![V=\pi (2r)^2(2h)=\pi (4r^2)(2h)=8\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20%282r%29%5E2%282h%29%3D%5Cpi%20%284r%5E2%29%282h%29%3D8%5Cpi%20r%5E2h)
So, compared to the old volume, the new volume is increased by eight-fold.
Statement 5 is not correct.