Question

Calculate the surface area of the cone shown.

Answer 1

No no no..
Area of the side is
\[\pi (5)(13)\]And the area of the base is
\[\pi (5^2)\]So the total is
\[\pi(25+65) = 90\pi\]

Answer 2

jacob check this out
http://math.about.com/od/formulas/ss/surfaceareavol_2.htm

Answer 3

Here's how to reason the surface area out: The surface area of the base is simple: \[A_1 =\pi(5)^2=25\pi\]The surface area of the rest of the cone is more difficult, however. The trick is to think of it unrolled, which will form a sector a circle. Take note that the sector of the circle will have radius 13. The area of this sector is a certain fraction of the area of a full circle with radius 13. Thus, the following proportion relating the area of the sector, the area of the full circle with radius 13, the length of the arc of the sector, and the circumference of the full circle with radius 13 holds:\[\dfrac{A_2}{\pi (13)^2}=\dfrac{2\pi(5)}{2\pi (13)}\]\[A_2=65\pi\] The total surface area is the sum of these two found values:\[A=25\pi+65\pi=90\pi\text{ }\checkmark\]