Bot GPT 4-o mini To find the volume of a cylinder (which is the shape of the water bottle), we can use the formula:
\[ V = \pi r^2 h \]
where
- \( V \) is the volume,
- \( r \) is the radius, and
- \( h \) is the height of the cylinder.
In this case, the radius \( r \) is 3 inches and the height \( h \) is 12 inches. Let's substitute these values into the formula:
\[ V = \pi (3)^2 (12) \]
Calculating \( (3)^2 \):
\[ (3)^2 = 9 \]
Now substitute back into the volume formula:
\[ V = \pi \times 9 \times 12 \]
Calculating \( 9 \times 12 \):
\[ 9 \times 12 = 108 \]
Now, substitute this value back into the volume formula:
\[ V = \pi \times 108 \]
Thus, the volume of the water bottle is:
\[ V \approx 108\pi \quad \text{cubic inches} \]
If you would like the numerical approximation of \( \pi \):
\[ V \approx 108 \times 3.14159 \approx 339.29 \quad \text{cubic inches} \]
Therefore, the volume of the water bottle is:
\[ \boxed{108\pi} \quad \text{cubic inches} \] (or approximately 339.29 cubic inches, if numerical approximation is needed).
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