To calculate the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \(V\) is the volume, \(r\) is the radius of the base, and \(h\) is the height of the cone.
In your case, the height \(h\) is 9 inches, and the base is a square with a side length of 5 inches. This means the base is not circular, and the usual formula for the volume of a cone does not apply. If we were to calculate the volume of a cone for a circular base, we would need the radius. However, given that the base is square, we need to clarify how the cone is defined.
If we assume you're asking about a cone that fits exactly inside a square base with a side length of 5 in, the radius of the circular base that the cone would inscribe would be \( \frac{5}{2} = 2.5 \) inches.
Now, substituting the values into the volume formula:
- Calculate \(r^2\):
\[ r^2 = (2.5)^2 = 6.25 \]
- Calculate the volume \(V\):
\[ V = \frac{1}{3} \times 3.14 \times 6.25 \times 9 \] \[ V = \frac{1}{3} \times 3.14 \times 56.25 \] \[ V = \frac{1}{3} \times 176.625 \] \[ V \approx 58.875 \]
Thus, the volume of the cone is approximately 58.88 cubic inches, which does not match any of the provided options.
Please verify the problem description—if the base is actually intended to be squared or if it's a misconception. If you were referring to something else, please provide that information!