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.
3,689.5 square centimeters
2,383.26 square centimeters
863.5 square centimeters
1,354.125 square centimeters
Surface Area of a Cone = πr(r + s)
Given:
Base diameter = 25 cm
Radius (r) = Base diameter / 2 = 25 / 2 = 12.5 cm
Height (h) = 22 cm
Slant height (s) = hypotenuse = 22 cm
So, we need to find the slant height (s) using the height (h) and radius (r) using the Pythagorean theorem:
s = sqrt(r^2 + h^2)
s = sqrt(12.5^2 + 22^2)
s = sqrt(156.25 + 484)
s = sqrt(640.25)
s ≈ 25.309
Plugging in the values:
Surface Area = 3.14 * 12.5(12.5 + 25.309)
Surface Area = 3.14 * 12.5 * 37.809
Surface Area ≈ 3.14 * 472.6125
Surface Area ≈ 1,483.11125 square centimeters
Therefore, the surface area of the cone is approximately 1,483.11 square centimeters.