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 m and the base has a circumference of 19.6 m, 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 19.6 m into the formula, we can solve for the radius:
19.6 = 2 * 3.14159 * r
Dividing both sides by 2 * 3.14159:
r = 19.6 / (2 * 3.14159)
r ≈ 3.1249 m
Now, substituting the values of the radius (approximately 3.1249 m) and height (9 m) into the volume formula:
V = (1/3) * 3.14159 * (3.1249)^2 * 9
Calculating the volume:
V ≈ (1/3) * 3.14159 * 3.1249^2 * 9
V ≈ 28.2669 cubic meters
Rounding to the nearest tenth of a cubic meter, the volume of the right circular cone is approximately 28.3 cubic meters.
