To find the volume of a spherical fish tank, you can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
In this case, the radius \( r \) is 3 inches. Plugging that into the formula gives:
\[ V = \frac{4}{3} \pi (3)^3 \]
Calculating \( (3)^3 \):
\[ (3)^3 = 27 \]
Now substitute back into the volume formula:
\[ V = \frac{4}{3} \pi \times 27 \]
Calculating \( \frac{4}{3} \times 27 \):
\[ \frac{4 \times 27}{3} = \frac{108}{3} = 36 \]
So the volume is:
\[ V = 36\pi \]
To find a numerical approximation, we can use \( \pi \approx 3.14 \):
\[ V \approx 36 \times 3.14 \approx 113.04 \text{ in}^3 \]
This is closest to the value in the options given (113.10 in³). Therefore, the volume of the fish tank when filled to the top is:
\[ \boxed{113.10 \text{ in}^3} \]
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