To find the volume of a bowl in the shape of a hemisphere, we can use the formula for the volume of a hemisphere:
\[ V = \frac{2}{3} \pi r^3 \]
Where \( r \) is the radius of the hemisphere and \( \pi \approx 3.14 \).
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Calculate the radius: The diameter of the bowl is 10.2 inches, so the radius \( r \) is half of the diameter:
\[ r = \frac{10.2}{2} = 5.1 \text{ inches} \]
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Calculate the volume using the radius: Substitute \( r \) and \( \pi \) into the volume formula:
\[ V = \frac{2}{3} \times 3.14 \times (5.1)^3 \]
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Calculate \( (5.1)^3 \): \[ (5.1)^3 = 5.1 \times 5.1 \times 5.1 = 132.651 \]
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Plug this value into the volume formula: \[ V = \frac{2}{3} \times 3.14 \times 132.651 \] \[ V = \frac{2 \times 3.14 \times 132.651}{3} \]
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Calculate \( 2 \times 3.14 \): \[ 2 \times 3.14 = 6.28 \]
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Multiply by \( 132.651 \): \[ 6.28 \times 132.651 \approx 833.773 \]
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Divide by 3: \[ V \approx \frac{833.773}{3} \approx 277.924 \]
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Round to the nearest whole number: The volume of the bowl is approximately 278 cubic inches.
Thus, the bowl can hold approximately 278 cubic inches of broth.
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