To find the volume of each cylinder, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cylinder.
-
Left Cylinder:
- Height \( h = 2 \)
- Diameter \( d = 3 \), so the radius \( r = \frac{d}{2} = \frac{3}{2} = 1.5 \)
Now plug in the values:
\[ V_{\text{left}} = \pi (1.5)^2 (2) = \pi (2.25)(2) = \pi (4.5) = 4.5\pi \]
-
Right Cylinder:
- Height \( H = 6 \)
- Diameter \( D = 3 \), so the radius \( R = \frac{D}{2} = \frac{3}{2} = 1.5 \)
Now plug in the values:
\[ V_{\text{right}} = \pi (1.5)^2 (6) = \pi (2.25)(6) = \pi (13.5) = 13.5\pi \]
-
Comparison:
- Volume of the left cylinder: \( 4.5\pi \)
- Volume of the right cylinder: \( 13.5\pi \)
The left and right cylinders do not have the same volume; the right cylinder has a volume that is three times that of the left cylinder. Specifically, the left cylinder has a volume of \( 4.5\pi \) cubic units, while the right cylinder has a volume of \( 13.5\pi \) cubic units.