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)

Answer 1

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Answer 2

First, we need to convert the measurements from feet to centimeters since the surface area is required in square centimeters.

We know that 1 foot is equal to 30.48 centimeters.

So, the diameter of the cone in centimeters is:
12 feet x 30.48 centimeters/foot = 365.76 centimeters (rounded to the nearest hundredth).

And the slant height of the cone in centimeters is:
14 feet x 30.48 centimeters/foot = 426.72 centimeters (rounded to the nearest hundredth).

The formula to find the lateral surface area of a cone is:
Lateral Surface Area = π*r*l
where r is the radius and l is the slant height.

Since we are given the diameter, we can find the radius.
The radius of the cone is half of the diameter, so:
Radius = 365.76 centimeters / 2 = 182.88 centimeters (rounded to the nearest hundredth).

Now we can calculate the surface area of the cone:
Surface Area = π*r*l
= 3.14 x 182.88 centimeters x 426.72 centimeters
= 234,832.36576 square centimeters
≈ 234,832.4 square centimeters (rounded to the nearest tenth).

Therefore, the surface area of the cone is approximately 234,832.4 square centimeters.