Use the image to answer the 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
1,354.125 square centimeters
1,354.125 square centimeters
3,689.5 square centimeters
To find the surface area of a cone, you need to find the area of the base and the lateral surface.
The base diameter is 25 centimeters, so the radius is half of that, which is 25/2 = 12.5 centimeters.
The area of the base is pi * radius^2 = 3.14 * 12.5^2 = 3.14 * 156.25 = 490.625 square centimeters.
The hypotenuse of the cone is the slant height, which is also the radius of the cone.
Using the Pythagorean theorem, we can find the height of the cone:
height^2 = hypotenuse^2 - base^2
height^2 = 22^2 - 12.5^2
height^2 = 484 - 156.25
height^2 = 327.75
height = sqrt(327.75) = 18.12 centimeters.
The lateral surface area is given by the formula pi * radius * slant height, so:
lateral surface area = 3.14 * 12.5 * 18.12 = 690.51 square centimeters.
Adding the base area and the lateral surface area, we get the total surface area:
Total surface area = base area + lateral surface area = 490.625 + 690.51 = 1181.135 square centimeters.
Therefore, the surface area of the cone is approximately 1181.135 square centimeters.