To find the volume of Kairay's sculpture, we first need to calculate the volume of the larger hemisphere with a radius of 20 inches and then subtract the volume of the smaller hemisphere with a radius of 15 inches.
The formula for the volume \( V \) of a hemisphere is given by:
\[ V = \frac{2}{3} \pi r^3 \]
For the larger hemisphere with a radius of 20 inches:
\[ V_{\text{large}} = \frac{2}{3} \pi (20^3) = \frac{2}{3} \pi (8000) = \frac{16000}{3} \pi \]
Substituting \( \pi \) with 3.14:
\[ V_{\text{large}} = \frac{16000}{3} \times 3.14 \approx 16755.56 , \text{in}^3 \]
For the smaller hemisphere with a radius of 15 inches:
\[ V_{\text{small}} = \frac{2}{3} \pi (15^3) = \frac{2}{3} \pi (3375) = \frac{6750}{3} \pi \]
Again, substituting \( \pi \) with 3.14:
\[ V_{\text{small}} = \frac{6750}{3} \times 3.14 \approx 7068.75 , \text{in}^3 \]
Now, to calculate the volume of the sculpture, we subtract the volume of the smaller hemisphere from the volume of the larger hemisphere:
\[ V_{\text{sculpture}} = V_{\text{large}} - V_{\text{small}} \approx 16755.56 - 7068.75 \approx 9686.81 , \text{in}^3 \]
Rounding this to the nearest whole number, we get:
\[ \boxed{9687 , \text{in}^3} \]
Among the options provided, the closest answer is: 9,682 inches cubed.