To calculate the volume \( V \) of a cone, you use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14.
In this case, the radius \( r \) is 5 inches and the height \( h \) is 15 inches. Plugging in the values:
\[ V = \frac{1}{3} \times 3.14 \times (5^2) \times 15 \]
Calculating step by step:
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Calculate \( r^2 \): \[ 5^2 = 25 \]
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Substitute into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 25 \times 15 \]
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Calculate \( 25 \times 15 \): \[ 25 \times 15 = 375 \]
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Now substitute this back: \[ V = \frac{1}{3} \times 3.14 \times 375 \]
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Calculate \( 3.14 \times 375 \): \[ 3.14 \times 375 = 1177.5 \]
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Finally, divide by 3: \[ V = \frac{1177.5}{3} = 392.5 \]
Thus, the volume of the vase is \( \boxed{392.5} \) cubic inches.