Respuesta :
Answer:
213.69 units
Step-by-step explanation:
We have to first find the height of the cone.
We can use Pythagoras rule because the slant height, height and radius of a cone all form a right angled triangle:
[tex]h^2 = a^2 + b^2[/tex]
where h = hypotenuse
a and b = the other two sides of the triangle
The radius is 4 units and the slant height is 13 units:
[tex]13^2 = a^2 + 4^2\\\\169 = a^2 + 16\\\\a^2 = 169 - 16 = 153\\\\a = \sqrt{153}\\\\a = 12.37units[/tex]
The height of the cone is 12.37 units.
The surface area of a cone is given as:
SA = [tex]\pi r (r + \sqrt{h^2 + r^2} )[/tex]
[tex]SA = \pi * 4(4 + \sqrt{12.37^2 + 4^2} )\\\\SA = 12.57(4 + \sqrt{13^2} )\\SA = 12.57 (4 + 13)\\\\SA = 12.57(17)\\\\SA = 213.69 units[/tex]
The surface area of the cone is 213.69 units.
