To find the volume of the rectangular prism, we can use the formula for the volume of a rectangular prism:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given:
- Length = 6 inches
- Width = 4.5 inches
- Height = 2 inches
Now, plug in the values:
\[ V = 6 \times 4.5 \times 2 \]
Calculating this step-by-step:
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Calculate \(6 \times 4.5\): \[ 6 \times 4.5 = 27 \]
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Now, multiply by the height (2): \[ 27 \times 2 = 54 \]
So, the volume of the rectangular prism is 54 cubic inches.
Next, we will find the volume of the hemisphere that is cut out. The formula for the volume of a hemisphere is:
\[ V = \frac{2}{3} \pi r^3 \]
Where \(r\) is the radius. The diameter of the hemisphere is 2.5 inches, so the radius \(r\) is:
\[ r = \frac{2.5}{2} = 1.25 \text{ inches} \]
Now, calculate the volume of the hemisphere:
\[ V = \frac{2}{3} \pi (1.25)^3 \]
Calculating \( (1.25)^3 \):
\[ 1.25^3 = 1.25 \times 1.25 \times 1.25 = 1.953125 \]
Now, substituting this value into the hemisphere volume formula:
\[ V = \frac{2}{3} \pi (1.953125) \]
Using \(\pi \approx 3.14159\):
\[ V \approx \frac{2}{3} \times 3.14159 \times 1.953125 \approx \frac{2 \times 3.14159 \times 1.953125}{3} \]
Calculating:
\[ \approx \frac{12.281158}{3} \approx 4.093719 \text{ cubic inches} \]
To find the final volume of the mold, we subtract the volume of the hemisphere from the volume of the rectangular prism:
\[ V_{\text{mold}} = V_{\text{prism}} - V_{\text{hemisphere}} = 54 - 4.093719 \approx 49.906281 \]
Rounding this to the nearest tenth gives:
\[ \approx 49.9 \text{ cubic inches} \]
Thus, the final answer is:
49.9 in.³