Question

Find the volume of the cone. Round your answer to the nearest whole number.

1. Height: 7 ft
Volume: \(183^{3}\) ft

Answer 1

[AI-generated answer — Bot GPT 3.5]

Volume of a cone formula: \(V = \frac{1}{3}\pi r^{2} h\)

Given volume: \(183^{3} ft\)

Let's find the radius, \(r\), using the given volume:
\(V = \frac{1}{3}\pi r^{2} h\)
\(183^{3} = \frac{1}{3}\pi r^{2} \times 7\)
\(549 = \pi r^{2} \times 7\)
\(r^{2} = \frac{549}{7\pi}\)
\(r^{2} \approx 24.84\)
\(r \approx 4.98\) ft

Now we can find the volume using \(r = 4.98\) ft and \(h = 7\) ft:
\(V = \frac{1}{3}\pi (4.98)^{2} \times 7\)
\(V = \frac{1}{3}\pi (24.80) \times 7\)
\(V \approx 164 ft^{3}\)

Rounding to the nearest whole number, the volume of the cone is approximately 164 cubic feet.