Find the volume of a right circular cone that has a height of 9 cm and a base with a circumference of 16.9 cm. Round your answer to the nearest tenth of a cubic centimeter.
To find the volume of a cone, we will use the formula: V = (1/3) * π * r^2 * h
Given:
Height (h) = 9 cm
Circumference of base = 16.9 cm
Since the circumference of the base is 2πr, we can find the radius:
2πr = 16.9 cm
r = 16.9 / (2π) = 16.9 / (2 * 3.14159) ≈ 2.69 cm
Now we can plug the values into the formula:
V = (1/3) * π * (2.69)^2 * 9
V ≈ (0.333) * 3.14159 * 7.2361 * 9
V ≈ 67.976
Rounded to the nearest tenth, the volume of the cone is approximately 68.0 cubic centimeters.