To calculate the volume of Kairay's sculpture, we need to find the volume of the larger hemisphere (with a radius of 20 inches) and subtract the volume of the smaller hemisphere (with a radius of 15 inches) from it.
The formula for the volume \( V \) of a hemisphere with radius \( r \) is:
\[ V = \frac{2}{3} \pi r^3 \]
Step 1: Calculate the volume of the larger hemisphere (radius = 20 inches)
\[ V_{large} = \frac{2}{3} \cdot 3.14 \cdot (20)^3 \]
Calculating \( (20)^3 \):
\[ (20)^3 = 8000 \]
Now substituting back into the volume formula:
\[ V_{large} = \frac{2}{3} \cdot 3.14 \cdot 8000 \]
Calculating:
\[ V_{large} = \frac{2 \cdot 3.14 \cdot 8000}{3} = \frac{50240}{3} \approx 16746.67 \]
Step 2: Calculate the volume of the smaller hemisphere (radius = 15 inches)
\[ V_{small} = \frac{2}{3} \cdot 3.14 \cdot (15)^3 \]
Calculating \( (15)^3 \):
\[ (15)^3 = 3375 \]
Now substituting back into the volume formula:
\[ V_{small} = \frac{2}{3} \cdot 3.14 \cdot 3375 \]
Calculating:
\[ V_{small} = \frac{2 \cdot 3.14 \cdot 3375}{3} = \frac{21165}{3} \approx 7055 \]
Step 3: Calculate the volume of the sculpture
Now we will subtract the volume of the smaller hemisphere from the larger hemisphere:
\[ V_{sculpture} = V_{large} - V_{small} \]
Substituting the values we found:
\[ V_{sculpture} \approx 16746.67 - 7055 \approx 9691.67 \]
Rounding to the nearest whole number gives us:
\[ V_{sculpture} \approx 9692 \]
Since this value is not in the provided answer choices, let’s analyze the options presented. The closest matching option (and the only one reasonably close) is 9,682.
Thus, the answer is:
1. 9,682 in³
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