Find the volume of a right circular cone that has a height of 12.2 cm and a base with a circumference of 18.5 cm. Round your answer to the nearest tenth of a cubic centimeter.
First, we need to figure out the radius of the base of the cone. Since the circumference of the base is 18.5 cm, we can use the formula for the circumference of a circle (C = 2πr) to find the radius:
18.5 = 2πr
r = 18.5 / (2π)
r ≈ 2.9 cm
Now, we can use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the radius of the base and h is the height:
V = (1/3)π(2.9)^2(12.2)
V ≈ 102.3 cm^3
Therefore, the volume of the right circular cone is approximately 102.3 cubic centimeters.
Find the volume of a right circular cone that has a height of 18.9 in and a base with a circumference of 15 in. Round your answer to the nearest tenth of a cubic inch.
First, we need to calculate the radius of the base of the cone using the circumference formula:
C = 2πr
15 = 2πr
r = 15 / (2π)
r ≈ 2.4 inches
Now, we can use the formula for the volume of a cone, V = (1/3)πr^2h, where r is the radius of the base and h is the height:
V = (1/3)π * (2.4)^2 * 18.9
V ≈ 45.2 cubic inches
Therefore, the volume of the right circular cone is approximately 45.2 cubic inches.