So first of all, to solve this, we need to know the formula for finding the surface area of a cone. The formula is :
\(SA = \pi r(r+ \sqrt{ h^{2} + r^{2} } )\)
Where SA stands for surface area, h stands for height, and r stands for radius.
In the given information, we are not told the height, but we are told the slant height.
In a cone, the slant height, the height, and the radius together form a right triangle. We can use that triangle to solve for the height
So, to find the height, we can do:
5^2+b^2 = 12^2, or 25+b^2 = 144
Therefore, b is equal to about 11
So now, we can plug all of our values into the formula
This gives us:
\(SA = \pi * 5 (5+ \sqrt{ 5^{2} + 11^{2} } )\)
If we solve, this gives us about 267.
Therefore the answer is 267 feet squared
Hope this helped!! :D
