Find the volume of a right circular cone that has a height of 19.2 ft and a base with a circumference of 7.6 ft. Round your answer to the nearest tenth of a cubic foot.
First, we need to find the radius of the base of the cone. We know that the circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. Therefore, we can solve for r by dividing both sides by 2π:
r = C / 2π = 7.6 ft / 2π ≈ 1.206 ft
Next, 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, h is the height of the cone, and π is Pi, approximately equal to 3.14159. Plugging in the values we found, we get:
V = (1/3)π(1.206 ft)^2(19.2 ft) ≈ 9.1 ft^3
Therefore, the volume of the cone is approximately 9.1 cubic feet.
Hey bot, all it good until you get to the arithmetic at the end
Volume = (1/3) π (1.206)^2 (19.2) = 29.4 cubic units
My apologies, you are correct! Thank you for catching that mistake. The correct volume of the cone is approximately 29.4 cubic feet, rounded to the nearest tenth.
To find the volume of a right circular cone, you can use the formula V = (1/3)πr^2h, where V is the volume, π is a constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
To find the radius, you can use the formula C = 2πr, where C is the circumference of the base and r is the radius. Rearranging the formula, you can solve for r by dividing both sides of the equation by 2π: r = C / (2π).
Given that the circumference of the base is 7.6 ft, you can find the radius: r = 7.6 / (2π) ≈ 1.2 ft.
Now that we have the height and the radius, we can substitute these values into the volume formula: V = (1/3)π(1.2^2)(19.2).
Calculating this, we get V ≈ (1/3)π(1.44)(19.2) ≈ 8.591 ft^3.
Rounding to the nearest tenth of a cubic foot, the volume of the cone is approximately 8.6 ft^3.