Final answer:
The correct volume of a cone with the given measurements is approximately 296.96 cm³, which does not match with any of the options provided. It's important to check the calculations or the options given.
Step-by-step explanation:
To find the volume of a cone with a diameter of 8 centimeters and a height of 14 centimeters, we need to use the formula for the volume of a cone which is V = (1/3)πr²h, where r is the radius of the cone, h is the height, and π (pi) is approximately 3.14159.
Firstly, we need to find the radius of the cone. Since the diameter is 8 centimeters, the radius, which is half of the diameter, will be 4 centimeters. Now, we can plug the radius and the height into the formula:
V = (1/3)π(4 cm)²(14 cm)
= (1/3)π(16 cm²)(14 cm)
= (1/3)(3.14159)(16 cm²)(14 cm)
= 3.14159 × 16 cm² × 4.6667 cm
= 3.14159 × 74.6667 cm³
Approximately 296.96 cm³, which is not an option provided in the question. There might have been a mistake in the calculation or in the options provided. If we must choose from the given options, we should re-check our calculations or ask for clarification.