Find the volume of a right circular cone that has a height of 12.7 cm and a base with a diameter of 18.9 cm. Round your answer to the nearest tenth of a cubic centimeter.
The radius of the base of the cone is half the diameter, so it is 18.9 cm / 2 = <<18.9/2=9.45>>9.45 cm.
The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where V is the volume, π is a mathematical constant (approximately equal to 3.14159), r is the radius of the base, and h is the height.
Plugging in the given values, we have V = (1/3) * 3.14159 * (9.45 cm) ^ 2 * 12.7 cm.
Calculating, we find V ≈ 1/3 * 3.14159 * 89.3025 cm^2 * 12.7 cm = 374.16750375 cm^3.
Rounding to the nearest tenth, the volume is approximately 374.2 cm^3. Answer: \boxed{374.2}.
thats wrong bot
Apologies for the miscalculation. Let's calculate the volume correctly.
The radius of the base is half the diameter, so it is 18.9 cm / 2 = 9.45 cm.
The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where V is the volume, π is a mathematical constant (approximately equal to 3.14159), r is the radius of the base, and h is the height.
Plugging in the given values, we have V = (1/3) * 3.14159 * (9.45 cm)^2 * 12.7 cm.
Calculating, we find V ≈ 1/3 * 3.14159 * 89.3025 cm^2 * 12.7 cm = 1/3 * 3.14159 * 1133.48275 cm^3 ≈ 1/3 * 3563.58605927 cm^3 ≈ 1187.86202 cm^3.
Rounding to the nearest tenth, the volume is approximately 1187.9 cm^3. Answer: \boxed{1187.9}.
To find the volume of a right circular cone, we use the formula:
Volume = (1/3) * π * r^2 * h
Where:
- π represents the mathematical constant pi, approximately equal to 3.14159.
- r is the radius of the cone's base.
- h is the height of the cone.
First, we need to find the radius of the cone's base. The diameter is given as 18.9 cm, so to find the radius, we divide the diameter by 2:
Radius = Diameter / 2 = 18.9 cm / 2 = 9.45 cm
Now we have the radius (r = 9.45 cm) and the height (h = 12.7 cm), so we can plug in these values into the volume formula:
Volume = (1/3) * π * (9.45 cm)^2 * 12.7 cm
Simplifying the equation:
Volume = (1/3) * 3.14159 * (9.45 cm)^2 * 12.7 cm
Volume = 1.0472 * (89.3025 cm^2) * 12.7 cm
Volume = 11278.5287 cm^3
Rounding to the nearest tenth of a cubic centimeter:
Volume ≈ 11278.5 cm^3
Therefore, the volume of the right circular cone is approximately 11278.5 cubic centimeters.