You can put this solution on YOUR website! I presume that you are thinking of a right-circular cone ... that is, a cone whose height (h) is measured along a line perpendicular to the base that goes through the center of the circular base and through the vertex of the cone.
The formula for this surface area is:
where the variables in the equation are defined as: S is the surface area; r is the radius of the circle that forms the base; and s is the slant length of a line that goes from the perimeter of the circle forming the base to the vertex.
By the way of explanation the length of s is the hypotenuse of a right triangle whose legs are r and h where h is the length of the perpendicular between the center of the circular base and the vertex.
For your problem, you are given that the radius of the circular base is 10 feet and the height of the cone is 18 feet. From this calculate s using the Pythagorean theorem:
s =
s =
s =
s = 20.5913 ft
Next substitute the known values of the variables into the surface area formula:
When you do the multiplication you find that the surface area is 646.895 square feet.
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