Final answer:
To find the volume of a right circular cone with a given height and base circumference, divide the circumference by 2π to find the radius. Then, use the formula V = (1/3)πr²h to calculate the volume, substituting the values and rounding to the nearest tenth.
Step-by-step explanation:
To find the volume of a right circular cone, you can use the formula V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height of the cone. In this case, the height of the cone is 19.2 ft. Since the base has a circumference of 7.6 ft, we can find the radius (r) by dividing the circumference by 2π. Therefore, r = (7.6 ft)/(2π) = 1.21 ft. Substituting the values into the formula, we have V = (1/3)π(1.21 ft)²(19.2 ft). Evaluating the expression gives V ≈ 7.4 ft³. Rounding to the nearest tenth, the volume of the cone is approximately 7.4 cubic feet.