The volume \( V \) of a cone can be calculated using the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is a mathematical constant approximately equal to 3.14.
For this flower vase:
- The radius \( r = 5 \) inches,
- The height \( h = 15 \) inches.
Now substituting these values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (5)^2 \times 15 \]
Calculating \( (5)^2 \):
\[ (5)^2 = 25 \]
Now substitute 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 into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 375 \]
Calculating \( 3.14 \times 375 \):
\[ 3.14 \times 375 = 1177.5 \]
Now divide by 3:
\[ V = \frac{1177.5}{3} \approx 392.5 \]
Thus, the volume of water that the flower vase can hold is approximately \( 392.5 \) cubic inches.