To find out which vase has a greater volume, we can use the formula for the volume \( V \) of a cylinder, which is given by:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.
For the first vase:
- Height (\( h_1 \)) = 2
- Radius (\( r_1 \)) = 2
The volume \( V_1 \) is calculated as follows:
\[ V_1 = \pi (r_1^2)(h_1) = \pi (2^2)(2) = \pi (4)(2) = 8\pi \]
For the second vase:
- Height (\( h_2 \)) = 6
- Radius (\( r_2 \)) = 1
The volume \( V_2 \) is calculated as follows:
\[ V_2 = \pi (r_2^2)(h_2) = \pi (1^2)(6) = \pi (1)(6) = 6\pi \]
Now we can compare the two volumes:
- Volume of the first vase: \( 8\pi \)
- Volume of the second vase: \( 6\pi \)
Since \( 8\pi > 6\pi \), the first vase has a greater volume.
Thus, the first vase (height = 2, radius = 2) has more volume than the second vase (height = 6, radius = 1).
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