Answer:
See Explanation
Step-by-step explanation:
Given
The question is incomplete, as the cylinders are not given.
Required
The cylinder with greater volume
To answer this question, I will assume the following dimensions.
Cylinder 1
[tex]r = 5[/tex]
[tex]h = 10[/tex]
Cylinder 2
[tex]r = 7[/tex]
[tex]h = 5[/tex]
Volume is calculated as:
[tex]V = \pi r^2h[/tex]
When the radius is reduced by 2, the formula becomes
[tex]V = \pi (r - 2)^2h[/tex]
For the first cylinder, we have:
[tex]V_1 = \pi (r - 2)^2h[/tex]
[tex]V_1 = 3.14 * (5 - 2)^2 * 10[/tex]
[tex]V_1 = 3.14 * 3^2 * 10[/tex]
[tex]V_1 = 3.14 * 9 * 10\\[/tex]
[tex]V_1 = 282.6[/tex]
For the second cylinder, we have:
[tex]V_2 = \pi (r - 2)^2h[/tex]
[tex]V_2 = 3.14 * (7 - 2)^2 * 5[/tex]
[tex]V_2 = 3.14 * 5^2 * 5[/tex]
[tex]V_2 = 3.14 * 25 * 5[/tex]
[tex]V_2 = 392.5[/tex]
Cylinder 2 has a greater volume because 392.5 > 282.6
Note: Irrespective of the dimension of the cylinders, the above step works fine.
