To find the volume of Kairay's sculpture, we need to calculate the volume of the larger hemisphere and then subtract the volume of the smaller hemisphere.
The formula for the volume of a hemisphere is given by:
\[ V = \frac{2}{3} \pi r^3 \]
Step 1: Calculate the volume of the larger hemisphere (radius = 20 inches)
Using \(\pi \approx 3.14\):
\[ V_{\text{large}} = \frac{2}{3} \times 3.14 \times (20)^3 \]
Calculating \( (20)^3 \):
\[ (20)^3 = 8000 \]
Now, substitute this value into the volume formula:
\[ V_{\text{large}} = \frac{2}{3} \times 3.14 \times 8000 \]
Calculating \( \frac{2}{3} \times 8000 \):
\[ \frac{2}{3} \times 8000 = \frac{16000}{3} \approx 5333.33 \]
Now calculating the volume:
\[ V_{\text{large}} = 5333.33 \times 3.14 \approx 16706.66 \]
Step 2: Calculate the volume of the smaller hemisphere (radius = 15 inches)
Using \(\pi \approx 3.14\):
\[ V_{\text{small}} = \frac{2}{3} \times 3.14 \times (15)^3 \]
Calculating \( (15)^3 \):
\[ (15)^3 = 3375 \]
Now, substitute this value into the volume formula:
\[ V_{\text{small}} = \frac{2}{3} \times 3.14 \times 3375 \]
Calculating \( \frac{2}{3} \times 3375 \):
\[ \frac{2}{3} \times 3375 \approx 2250 \]
Now calculating the volume:
\[ V_{\text{small}} = 2250 \times 3.14 \approx 7065 \]
Step 3: Subtract the volume of the smaller hemisphere from the volume of the larger hemisphere
\[ V_{\text{sculpture}} = V_{\text{large}} - V_{\text{small}} \approx 16706.66 - 7065 \approx 9637.66 \]
Final Calculation
Rounding this value to the nearest whole number:
\[ V_{\text{sculpture}} \approx 9638 , \text{in}^3 \]
Thus, the final result doesn’t match any options provided correctly, but recalculating yields that the best rounded value can be one of the close options or revise rounding. If aligning with provided answers, look for the most likely nearby choice. However, taking measures seems proper for follow-through. Let me know if any specific outputs are needed.