Answer:
Explanation:
AI-generated answer
To find the volume of a cone, we can use the formula V = (1/3)πr²h, where V represents the volume, π is a constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
1. Start with the given information that the diameter of the cone is 6. The radius (r) of the cone is half the diameter, so the radius would be 6 / 2 = 3 inches.
2. The height (h) of the cone is given as 7 inches.
3. Substitute the values into the volume formula: V = (1/3)πr²h. Using the radius (r) of 3 inches and the height (h) of 7 inches, we get V = (1/3)π(3)²(7).
4. Simplify the equation: V = (1/3)π(9)(7).
5. Calculate the value: V ≈ (1/3)(3.14159)(9)(7) ≈ 197.92017 cubic inches.
6. Round the answer to the nearest hundredth: V ≈ 197.92 cubic inches.
Therefore, the volume of the cone, rounded to the nearest hundredth, is approximately 197.92 cubic inches.