To find the volume of a cone, we can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume
- \( r \) is the radius
- \( h \) is the height
- \( \pi \) is a constant approximately equal to 3.14
Given:
- Radius \( r = 5 \) inches
- Height \( h = 15 \) inches
- \( \pi \approx 3.14 \)
Let's plug in the values:
\[ V = \frac{1}{3} \times 3.14 \times (5)^2 \times (15) \]
Calculating \( (5)^2 \):
\[ (5)^2 = 25 \]
Now substituting this back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 25 \times 15 \]
Calculating \( 25 \times 15 \):
\[ 25 \times 15 = 375 \]
Now substituting this into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 375 \]
Calculating \( \frac{1}{3} \times 375 \):
\[ \frac{1}{3} \times 375 = 125 \]
Now multiply by 3.14:
\[ V = 125 \times 3.14 = 392.5 \]
Thus, the volume of the water that the flower vase can hold is
\[ \boxed{392.5} \text{ cubic inches} \]