Final answer:
The volume of the cone with a base diameter of 14 and height of 16 is 259.51 cubic units. The formula used is V = 1/3πr²h, with r as the radius.
Step-by-step explanation:
The student has asked for the volume of a cone with a given base diameter and height. To calculate the volume of a cone, we use the following formula:
V = ⅓πr²h
Where V is the volume, r is the radius of the base, and h is the height of the cone. Since the diameter of the base is 14, the radius (r) is half of that, which is 7. Therefore, we can substitute the values into the formula:
V = ⅓π(7²)(16)
V = ⅓π(49)(16)
V = ⅓(3.14159)(49)(16)
V = ⅓(772.54)
V = 259.51 cubic units
Thus, the volume of the cone is 259.51 cubic units.