A right cone shows a base diameter of 14 millimeters and a perpendicular height of 12 millimeters. A right angle is formed with the diameter and the height at the center of the circular base.
What is the volume, in cubic millimeters, of the cone? Round your answer to the nearest hundredth.
The radius of the cone's base can be found by dividing the diameter by 2. So, the radius is 14 mm / 2 = 7 mm.
The volume of a cone can be calculated using the formula V = (1/3) * π * r^2 * h, where V is the volume, π is pi (approximately 3.14), r is the radius, and h is the height.
Plugging in the given values, we have V = (1/3) * 3.14 * (7 mm)^2 * 12 mm.
Simplifying this expression, we get V = (1/3) * 3.14 * 49 mm^2 * 12 mm.
Calculating this expression, we get V ≈ 616 mm^3.
Therefore, the volume of the cone is approximately 616 cubic millimeters.