Answer :
Final answer:
To find the height of a cone given its volume and diameter, we first find the radius (half of the diameter), then use the formula for the volume of a cone to solve for the height. In this case, the approximate height of the cone is 6 inches.
Explanation:
The subject of this question is about finding the height of a cone given its diameter and volume using the formula for the volume of a cone. First, we need to find the radius of the cone, which is half of the diameter, so it's 1.5 inches in this case.
Then, we use the formula for the volume of a cone, which is (1/3)πr²h where r is the radius and h is the height. Since we know the volume is 12 cubic inches, and the radius is 1.5 inches, we substitute these values into the formula and solve for h to find the height of the cone.
So, the equation becomes (1/3)π*(1.5)²h = 12. Solving for h, we find that the height of the cone is approximately 6 inches, rounding to the nearest inch.
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