First, we need to convert the diameter from feet to centimeters. Since 1 foot is equal to 30.48 centimeters, the diameter of the cone is 12 feet * 30.48 centimeters/foot = <<12*30.48=365.76>>365.76 centimeters.
Next, we can calculate the radius of the cone by dividing the diameter by 2: radius = 365.76 centimeters / 2 = <<365.76/2=182.88>>182.88 centimeters.
Now, we can calculate the slant height of the cone in centimeters since the slant height is the hypotenuse of a right triangle formed by the slant height, the radius, and the height. Using the Pythagorean theorem, we have height^2 + radius^2 = slant height^2.
Solving for the height, we get height = sqrt(slant height^2 - radius^2) = sqrt(14 feet * 30.48 centimeters/foot)^2 - (182.88 centimeters)^2 = sqrt(42614.56) = 206.37 centimeters.
Next, we can calculate the lateral surface area of the cone using the formula SA = pi * radius * slant height = 3.14 * 182.88 centimeters * 206.37 centimeters = 117,369.15 square centimeters. Answer: \boxed{117,369.15}.
What is the surface area, in square centimeters, of a cone with a diameter of 12 feet and a slant height of 14 feet? Use 3.14 for pi and round to the nearest tenth, if necessary. .
3 answers
What
I apologize for the error in my previous response. Let's re-calculate the surface area of the cone.
The diameter of the cone is 12 feet, which means the radius is half of that, so the radius is 12 feet / 2 = 6 feet.
To convert the feet to centimeters, we multiply by the conversion factor of 30.48: 6 feet * 30.48 cm/foot = 182.88 cm.
The slant height of the cone is given as 14 feet, so we convert that to centimeters: 14 feet * 30.48 cm/foot = 426.72 cm.
The lateral surface area of a cone is given by the formula A = πrℓ, where r is the radius and ℓ is the slant height.
Plugging in the calculated values, we get A = 3.14 * 182.88 cm * 426.72 cm ≈ 234,576.50336 cm². Rounding to the nearest tenth, the surface area is approximately 234,576.5 cm².
The diameter of the cone is 12 feet, which means the radius is half of that, so the radius is 12 feet / 2 = 6 feet.
To convert the feet to centimeters, we multiply by the conversion factor of 30.48: 6 feet * 30.48 cm/foot = 182.88 cm.
The slant height of the cone is given as 14 feet, so we convert that to centimeters: 14 feet * 30.48 cm/foot = 426.72 cm.
The lateral surface area of a cone is given by the formula A = πrℓ, where r is the radius and ℓ is the slant height.
Plugging in the calculated values, we get A = 3.14 * 182.88 cm * 426.72 cm ≈ 234,576.50336 cm². Rounding to the nearest tenth, the surface area is approximately 234,576.5 cm².
2 answers