Question

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

Answer 1

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Answer 2

oops i forgot i had caps on... can you please try again?

Answer 3

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.