To find the volume of a right circular cone, we can use the formula:
V = (1/3) * π * r^2 * h
where V is the volume, r is the radius of the base, and h is the height of the cone.
Given that the height of the cone is 9 cm and the base has a circumference of 16.9 cm, we can find the radius of the base.
The circumference of a circle is given by the formula:
C = 2 * π * r
Substituting the given circumference of 16.9 cm into the formula, we can solve for the radius:
16.9 = 2 * 3.14159 * r
Dividing both sides by 2 * 3.14159:
r = 16.9 / (2 * 3.14159)
r ≈ 2.6878 cm
Now, substituting the values of the radius (approximately 2.6878 cm) and height (9 cm) into the volume formula:
V = (1/3) * 3.14159 * (2.6878)^2 * 9
Calculating the volume:
V ≈ (1/3) * 3.14159 * 2.6878^2 * 9
V ≈ 64.1186 cubic centimeters
Rounding to the nearest tenth of a cubic centimeter, the volume of the right circular cone is approximately 64.1 cubic centimeters.
