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.
First, we need to find the radius of the base of the cone. To do this, we can use the Pythagorean theorem:
r^2 + h^2 = l^2
r^2 + 25^2 = 22^2
r^2 + 625 = 484
r^2 = 484 - 625
r^2 = 121
r = 11
Now that we have the radius, we can calculate the surface area of the cone:
Surface Area = πr(r + l)
Surface Area = 3.14 * 11(11 + 22)
Surface Area = 3.14 * 11(33)
Surface Area = 3.14 * 363
Surface Area ≈ 1139.82 square centimeters
Therefore, the surface area of the cone is approximately 1139.82 square centimeters.