What is the surface area of a cone with a diameter of 25cm and a slant height of 22cm
The radius of the base of the cone is half of its diameter, so it is 25 cm / 2 = 12.5 cm.
The slant height forms a right triangle with the height and the radius of the base of the cone.
Using the Pythagorean theorem, we can find the height of the cone:
(Height)^2 + (Radius)^2 = (Slant height)^2
Height^2 + 12.5^2 = 22^2
Height^2 + 156.25 = 484
Height^2 = 327.75
Height ≈ 18.11 cm
The surface area of the cone is πr(r + l), where r is the radius and l is the slant height.
Surface area = π * 12.5 * (12.5 + 22)
Surface area ≈ 929.2 cm²
Therefore, the surface area of the cone is approximately 929.2 cm².