How much water is in a spherical-shaped fish tank with a radius of 3 if it is filled to the top?

113.10 in3
3
113.10 in3

63.62 in3
3
63.62 in3

12.57 in3
3
12.57 in3

123.15 in3

1 answer

To find the volume of a spherical fish tank, we 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.

Given that the radius \( r \) is 3 inches, we can plug this value into the formula:

\[ V = \frac{4}{3} \pi (3)^3 \]

Calculating \( (3)^3 \):

\[ (3)^3 = 27 \]

Now substituting back into the volume formula:

\[ V = \frac{4}{3} \pi (27) \]

\[ V = \frac{108}{3} \pi \]

\[ V = 36 \pi \]

Now we can use the value of \( \pi \) (approximately 3.14):

\[ V \approx 36 \times 3.14 \approx 113.04 , \text{in}^3 \]

This value is very close to 113.10 in³. Thus, if the tank is filled to the top, the volume of water in the tank is approximately:

\[ \text{Volume} \approx 113.10 \text{ in}^3 \]

So the correct answer is 113.10 in³.