Use the image to answer the question.
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? Use 3.14 for pi. Round your answer to the nearest hundredth.(1 point)
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The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height. Since the diameter is given, we need to divide it by 2 to find the radius.
Given the diameter is 14 mm, the radius is 14/2 = 7 mm. The height is given as 12 mm.
Now we can plug the values into the formula:
V = (1/3)π(7)^2(12)
V ≈ (1/3)(3.14)(49)(12)
V ≈ (3.14)(588)
V ≈ 1848.72 mm^3
Therefore, the volume of the cone is approximately 1848.72 cubic millimeters.
My apologies for the error. Let's try solving it again.
Given:
Base diameter = 14 mm
Perpendicular height = 12 mm
Radius (r) = diameter/2 = 14/2 = 7 mm
Volume of cone = (1/3) * π * r^2 * h
Volume = (1/3) * 3.14 * 7^2 * 12
Volume = (1/3) * 3.14 * 49 * 12
Volume = (1/3) * 3.14 * 588
Volume = 6194.72 mm^3
Therefore, the volume of the cone is 6194.72 cubic millimeters.