Find the volume of a right circular cone that has a height of 16 m and a base with a circumference of 14.7 m. Round your answer to the nearest tenth of a cubic meter.
To find the volume of a cone, you can use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height.
Since we are given the circumference of the base, we can calculate the radius with the formula C = 2πr. Rearranging the formula to solve for r, we get:
14.7 = 2πr
r = 14.7 / (2π)
r ≈ 2.34 m
Now that we have the radius and height, we can plug these values into the volume formula:
V = (1/3)π(2.34)^2(16)
V ≈ 49.1 m^3
Therefore, the volume of the cone is approximately 49.1 cubic meters.