To calculate the volume of Kairay's sculpture, we need to find the volume of the larger hemisphere and subtract the volume of the smaller hemisphere.
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Volume of a hemisphere formula: \[ V = \frac{2}{3} \pi r^3 \] where \( r \) is the radius.
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Volume of the larger hemisphere (radius = 20 inches): \[ V_{\text{large}} = \frac{2}{3} \cdot 3.14 \cdot (20)^3 \] First, calculate \( (20)^3 \): \[ (20)^3 = 8000 \] Now, substituting this value: \[ V_{\text{large}} = \frac{2}{3} \cdot 3.14 \cdot 8000 \] \[ V_{\text{large}} = \frac{2 \cdot 3.14 \cdot 8000}{3} = \frac{50240}{3} \approx 16746.67 \]
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Volume of the smaller hemisphere (radius = 15 inches): \[ V_{\text{small}} = \frac{2}{3} \cdot 3.14 \cdot (15)^3 \] First, calculate \( (15)^3 \): \[ (15)^3 = 3375 \] Now, substituting this value: \[ V_{\text{small}} = \frac{2}{3} \cdot 3.14 \cdot 3375 \] \[ V_{\text{small}} = \frac{2 \cdot 3.14 \cdot 3375}{3} = \frac{21237.5}{3} \approx 7079.17 \]
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Volume of the sculpture (subtract the volumes): \[ V_{\text{sculpture}} = V_{\text{large}} - V_{\text{small}} \] \[ V_{\text{sculpture}} \approx 16746.67 - 7079.17 \approx 9667.5 \]
Rounding this to the nearest whole number: \[ V_{\text{sculpture}} \approx 9668 \text{ in}^3 \]
Given the responses available:
- 7,065 in.³
- 16,747 in.³
- 19,363 in.³
- 9,682 in.³.
The closest rounded answer to our calculation (9668 in.³) is 9,682 in.³.