To find the volume of Kairay's sculpture, we need to calculate the volume of the larger hemisphere and subtract the volume of the smaller hemisphere.
The volume \( V \) of a hemisphere is given by the formula:
\[ V = \frac{2}{3} \pi r^3 \]
Step 1: Calculate the volume of the larger hemisphere with a radius of 20 inches.
Using \( r = 20 \) inches:
\[ V_{large} = \frac{2}{3} \pi (20)^3 \] \[ = \frac{2}{3} \pi (8000) \] \[ = \frac{16000}{3} \pi \]
Using \( \pi \approx 3.14 \):
\[ V_{large} = \frac{16000}{3} \times 3.14 \approx \frac{16000 \times 3.14}{3} \approx \frac{50240}{3} \approx 16747 \text{ cubic inches} \]
Step 2: Calculate the volume of the smaller hemisphere with a radius of 15 inches.
Using \( r = 15 \) inches:
\[ V_{small} = \frac{2}{3} \pi (15)^3 \] \[ = \frac{2}{3} \pi (3375) \] \[ = \frac{6750}{3} \pi \]
Using \( \pi \approx 3.14 \):
\[ V_{small} = \frac{6750}{3} \times 3.14 \approx \frac{6750 \times 3.14}{3} \approx \frac{21195}{3} \approx 7065 \text{ cubic inches} \]
Step 3: Calculate the volume of the sculpture.
Now, we subtract the volume of the smaller hemisphere from the volume of the larger hemisphere:
\[ V_{sculpture} = V_{large} - V_{small} \] \[ = 16747 - 7065 = 9682 \text{ cubic inches} \]
Thus, the volume of Kairay's sculpture is approximately:
9,682 cubic inches.
The correct response is 9,682 in.³.