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.(1 point)
square centimeters
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To find the surface area of a cone, we need to find the lateral area and the base area and then add them together.
The lateral area of a cone can be found using the formula:
Lateral area = π × radius × slant height
First, we need to convert the given diameter of 12 feet into a radius by dividing it by 2:
Radius = Diameter/2 = 12 ft / 2 = 6 ft
Now we can calculate the lateral area:
Lateral area = 3.14 × 6 ft × 14 ft = 263.52 ft²
The base area of a cone can be found using the formula:
Base area = π × radius^2
The radius is already calculated as 6 ft:
Base area = 3.14 × (6 ft)^2 = 3.14 × 36 ft² = 113.04 ft²
To find the total surface area, we add the lateral area and the base area:
Surface area = Lateral area + Base area = 263.52 ft² + 113.04 ft² = 376.56 ft²
Since the question asks for the answer in square centimeters, we need to convert the surface area from square feet to square centimeters.
1 foot = 30.48 centimeters
Square feet to square centimeters conversion: 1 ft² = 30.48 cm × 30.48 cm = 929.0304 cm²
Surface area in square centimeters = 376.56 ft² × 929.0304 cm²/ft² ≈ 349831.629 cm²
Therefore, the surface area of the cone is approximately 349831.629 square centimeters.
To find the surface area of a cone, you need to know the radius and slant height.
1. First, convert the diameter of the cone from feet to centimeters. Since there are 2.54 centimeters in an inch and 12 inches in a foot, you can multiply the diameter (12 feet) by 2.54 to get the diameter in centimeters: 12 feet * 2.54 centimeters/foot = 30.48 centimeters.
2. Next, divide the diameter by 2 to get the radius. In this case, the radius is 30.48 centimeters / 2 = 15.24 centimeters.
3. Now, plug the values of the radius (15.24 centimeters) and slant height (14 feet) into the formula for the surface area of a cone:
Surface Area = π * r * (r + l)
where π is approximately 3.14, r is the radius, and l is the slant height.
Surface Area = 3.14 * 15.24 cm * (15.24 cm + 14 ft * 2.54 cm/ft)
4. Calculate the surface area:
Surface Area = 3.14 * 15.24 cm * (15.24 cm + 14 ft * 2.54 cm/ft)
Surface Area ≈ 3.14 * 15.24 cm * (15.24 cm + 35.56 cm)
Surface Area ≈ 3.14 * 15.24 cm * 50.8 cm
Surface Area ≈ 2431.2928 cm²
5. Rounded to the nearest tenth, the surface area of the cone is approximately 2431.3 square centimeters.