Explanation:
r is the radius
h is the height
l is the slant height
The area of the curved (lateral) surface of a cone = πrl
To begin with we need to find slant height of the cone, which is determined by using Pythagoras, since the cross section is a right triangle.
l² = h² + r²
l² = 11² + 5²
l² = 121 + 25
l = √146
l = 12.08cm
And the total surface area of the cone is:
SA = πr²+ πrl
SA = π · r · (r + l)
SA = π · 5 · (5 + 12.08)
SA = 3.14 * 5 * 17.08
SA = 268.156 cm²
Therefore, the total surface area of the cone is 268.156 cm2