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Question

A cone shows a base diameter of 25 centimeters, perpendicular height from the base to the top vertex at 90 degrees, and 22 centimeters as the hypotenuse or the side of the cone.

What is the surface area of the cone? Use 3.14 for pi.

(1 point)
Responses

2,383.26 square centimeters
2,383.26 square centimeters

863.5 square centimeters
863.5 square centimeters

3,689.5 square centimeters
3,689.5 square centimeters

1,354.125 square centimeters

Answer 1

To find the surface area of the cone, we need to calculate the lateral surface area and the base area separately.

The lateral surface area of a cone can be found using the formula: π * r * l, where r is the radius of the base and l is the slant height (in this case, the hypotenuse).

Given that the diameter of the base is 25 centimeters, the radius would be half of that: 25/2 = 12.5 cm.

Using the Pythagorean theorem, we can find the slant height (l):
h^2 + r^2 = l^2
Given that the height (h) is 22 centimeters, we can substitute the values:
22^2 + 12.5^2 = l^2
484 + 156.25 = l^2
640.25 = l^2
l ≈ 25.32 cm (rounded to 2 decimal places)

Now we can calculate the lateral surface area:
π * 12.5 * 25.32 ≈ 994.24 square centimeters (rounded to 2 decimal places)

To find the base area of the cone, we use the formula: π * r^2.
π * 12.5^2 ≈ 490.87 square centimeters (rounded to 2 decimal places)

Finally, we can add the lateral surface area to the base area to get the total surface area of the cone:
994.24 + 490.87 ≈ 1,485.11 square centimeters (rounded to 2 decimal places)

Therefore, the correct answer is not given in the options provided.

Answer 2

but choose one though

Answer 3

If I have to choose one of the given options, the closest surface area to the calculated result would be:

1,354.125 square centimeters.

However, please note that this is not the exact surface area of the cone based on the given dimensions.