Unit Posttest \[ \begin{array}{l}\text { Jake volunteers to help out his younger brother's basketball team in his free time. One of his tasks is to ensure that all the basketballs have enough air } \\ \text { in them. Given that a properly inflated basketball measures } 8.8 \text { inches across, what is the total volume of air inside six of Jake's basketballs? Assume } \\ \text { that the wall of each ball is infinitely thin. } \\ \text { A. } 681.47 \pi \text { cubic inches } \\ \text { B. } 1,651.32 \pi \text { cubic inches } \\ \text { C. } 3,775.23 \pi \text { cubic inches } \\ \text { D. } 5,451.78 \pi \text { cubic inches }\end{array} \]

To find the total volume of air inside six properly inflated basketballs, we first need to calculate the volume of one basketball. The formula for the volume \( V \) of a sphere is given by: \[ V = \frac{4}{3} \pi r^3 \] Here, the diameter of the basketball is 8.8 inches, so the radius \( r \) is half of that: \[ r = \frac{8.8}{2} = 4.4 \text{ inches} \] Now we can calculate the volume of one basketball: \[ V = \frac{4}{3} \pi (4.4)^3 \] Calculating \( (4.4)^3 \): \[ (4.4)^3 = 85.184 \] Now substituting back into the volume formula: \[ V = \frac{4}{3} \pi (85.184) \approx 113.69 \pi \text{ cubic inches} \] Since we want the total volume for six basketballs, we multiply this by 6: \[ \text{Total Volume} = 6 \times 113.69 \pi \approx 682.14 \pi \text{ cubic inches} \] Among the provided choices, the closest value is approximately \( 681.47 \pi \text{ cubic inches} \). So the answer is: **A. 681.47 π cubic inches**