Jevonte measure the volume of a sink basin by modeling it as a hemisphere. Jevonte mea its radius to be \( 12 \frac{3}{4} \) inches. Find the sink's volume in cubic inches. Round your answer to nearest tenth if necessary.

To calculate the volume of a hemisphere, you can use the formula: \[ V = \frac{2}{3} \pi r^3 \] First, convert the radius \( 12 \frac{3}{4} \) inches into an improper fraction: \[ 12 \frac{3}{4} = \frac{51}{4} \text{ inches} \] Now plug this radius into the volume formula: \[ V = \frac{2}{3} \pi \left(\frac{51}{4}\right)^3 \] Calculating \( \left(\frac{51}{4}\right)^3 \): \[ \left(\frac{51}{4}\right)^3 = \frac{132651}{64} \] Now substitute this into the volume formula: \[ V = \frac{2}{3} \pi \cdot \frac{132651}{64} = \frac{265302 \pi}{192} \] Using \( \pi \approx 3.14 \): \[ V \approx \frac{265302 \times 3.14}{192} \approx 4334.68 \] Rounding to the nearest tenth, the volume of the sink basin is approximately: \[ \boxed{4334.7} \text{ cubic inches} \]