To determine how many cubic inches of water a spherical water balloon with a radius of 6 inches will hold, we need to calculate the volume of the sphere. The formula for the volume [tex]\(V\)[/tex] of a sphere is given by:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where:
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159,
- [tex]\( r \)[/tex] is the radius of the sphere.
Given that the radius [tex]\( r \)[/tex] is 6 inches, we can substitute this value into the formula:
[tex]\[ V = \frac{4}{3} \pi (6)^3 \][/tex]
First, calculate [tex]\( 6^3 \)[/tex]:
[tex]\[ 6^3 = 6 \times 6 \times 6 = 216 \][/tex]
Next, substitute [tex]\( 216 \)[/tex] into the volume formula:
[tex]\[ V = \frac{4}{3} \pi \times 216 \][/tex]
Multiply [tex]\( \frac{4}{3} \)[/tex] by [tex]\( 216 \)[/tex]:
[tex]\[ \frac{4}{3} \times 216 = 288 \][/tex]
Then, multiply [tex]\( 288 \)[/tex] by [tex]\( \pi \)[/tex] (approximately 3.14159):
[tex]\[ V = 288 \times \pi \approx 288 \times 3.14159 \approx 904.7786842338603 \][/tex]
Therefore, the volume of the spherical water balloon is approximately 904.78 cubic inches. None of the provided answer choices (288 in³, 78 in³, 144 in³, 214 in³) match the calculated volume. Hence, the correct selection is:
[tex]\[ \boxed{\text{There is no correct answer given.}} \][/tex]
