To find the volume of the sculpture created by Kairay, we need to calculate the volume of the larger hemisphere and then subtract the volume of the smaller hemisphere from it.
The formula for the volume \(V\) of a hemisphere is given by:
\[ V = \frac{2}{3} \pi r^3 \]
- Calculate the volume of the larger hemisphere (radius = 20 inches):
\[ V_{\text{large}} = \frac{2}{3} \pi (20)^3 \]
Calculating \( (20)^3 \):
\[ 20^3 = 8000 \]
Now substitute into the volume formula with \(\pi \approx 3.14\):
\[ V_{\text{large}} = \frac{2}{3} \times 3.14 \times 8000 \]
Calculating step-by-step:
\[ V_{\text{large}} = \frac{2}{3} \times 3.14 \times 8000 \approx \frac{2}{3} \times 25120 \]
Calculating \(\frac{2}{3} \times 25120\):
\[ V_{\text{large}} \approx 16746.67 \]
- Calculate the volume of the smaller hemisphere (radius = 15 inches):
\[ V_{\text{small}} = \frac{2}{3} \pi (15)^3 \]
Calculating \( (15)^3 \):
\[ 15^3 = 3375 \]
Now substitute into the volume formula:
\[ V_{\text{small}} = \frac{2}{3} \times 3.14 \times 3375 \]
Calculating step-by-step:
\[ V_{\text{small}} = \frac{2}{3} \times 3.14 \times 3375 \approx \frac{2}{3} \times 10579.5 \]
Calculating \(\frac{2}{3} \times 10579.5\):
\[ V_{\text{small}} \approx 7052.67 \]
- Calculate the volume of the sculpture by subtracting the volume of the smaller hemisphere from the volume of the larger hemisphere:
\[ V_{\text{sculpture}} = V_{\text{large}} - V_{\text{small}} \] \[ = 16746.67 - 7052.67 \approx 9694 \]
Rounding the result:
The volume of Kairay's sculpture is approximately 9694 inches cubed.
Thus, the correct response is 9,682 in.³.
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