Answer: [tex]\frac{1}{6}[/tex] or [tex]1:6[/tex]
Step-by-step explanation:
The volume of a cylinder can be found with the following formula:
[tex]V=\pi r^2h[/tex]
Where "r" is the radius and "h" is the height of the cylinder.
In this case, let be:
- [tex]V_1[/tex] the volume of one of this cylinders and [tex]V_2[/tex] the volume of the other one.
- [tex]r_1[/tex] the radius of the first one and [tex]r_2[/tex] the radius of the other cylinder.
- [tex]h_1[/tex] the height of one of them and [tex]h_2[/tex] the height of the other cylinder.
Then:
[tex]V_1=\pi r_1^2h_1\\\\V_2=\pi r_2^2h_2[/tex]
Therefore, you know this:
[tex]\frac{V_1}{V_2} =\frac{\pi r_1^2h_1}{\pi r_2^2h_2}[/tex]
Simplifying, you get:
[tex]\frac{V_1}{V_2} =\frac{ r_1^2h_1}{ r_2^2h_2}[/tex]
Now, knowing the ratios given in the exercise, you can substitute them into the equation:
[tex]\frac{V_1}{V_2} =\frac{1^2*2}{ 2^2*3}[/tex]
Evaluating, you get:
[tex]\frac{V_1}{V_2} =\frac{2}{ 4*3}\\\\\frac{V_1}{V_2} =\frac{2}{12}\\\\\frac{V_1}{V_2} =\frac{1}{6}[/tex]
