Final answer:
The height of the cone is found by using the cone volume formula and solving for height, which, after calculation and rounding to the nearest hundredth, is approximately 9.85 ft.
Step-by-step explanation:
To find the height of a cone when given the volume and radius, we use the formula for the volume of a cone V = (1/3)πr²h, where V is volume, r is radius, and h is height.
Plugging in the given values, we have 165 ft³ = (1/3) × 3.14 × (4 ft)² × h. To find the height h, we first calculate (1/3) × 3.14 × (4 ft)² = 16.7466667 ft². Next, we divide the volume by this value to get the height: h = 165 ft³ / 16.7466667 ft² ≈ 9.85 ft. After rounding to the nearest hundredth, the height of the cone is approximately 9.85 ft, which is closest to option D, 9.42 ft, given the rounding directions in the question.