Question

The height of the cone is 9 in
The base of the cone is 5 in
The corner of the cone is a square

What is the volume of the cone? Use 3.14 for pi.

(1 point)

423.9 cubic inches

47.1 cubic inches

235.5 cubic inches

942 cubic inches

Answer 1

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:

1. Calculate \(r^2\):

\[
r^2 = (2.5)^2 = 6.25
\]

2. 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!