The equation for the surface area of cylinder is
![SA = 2 \pi rh+2 \pi r^{2}](https://tex.z-dn.net/?f=SA%20%3D%202%20%5Cpi%20rh%2B2%20%5Cpi%20r%5E%7B2%7D%20)
, where SA = surface area, r = radius, and h = height.
To help you remember this equation, remember that the surface area is the total area of all the surfaces of a shape. A cylinder is made up of two circles and a long rectangle that creates the body of the cylinder (see picture). The surface area is thus the area of the two circles (
![2 \times \pi r^{2}](https://tex.z-dn.net/?f=2%20%5Ctimes%20%5Cpi%20r%5E%7B2%7D)
) plus the area of the rectangle (
![2 \pi r \times h](https://tex.z-dn.net/?f=2%20%5Cpi%20r%20%5Ctimes%20h)
), which has a width of 2<span>πr (aka the circumference of a circle) and a height of h.
Back to the problem:
You are told that the diameter of the cylinder is 5in. Remember that the diameter = 2r (2 times the radius). That means the radius, r = 5/2 = 2.5 in. You are also told the height, h = 4in. Plug these values into the equation for the surface area of a cylinder:
</span>
![SA = 2 \pi rh+2 \pi r^{2} \\ SA = 2 \pi (2.5)(4)+2 \pi (2.5)^{2}\\ SA \approx 102.1 \: in^{2}](https://tex.z-dn.net/?f=SA%20%3D%202%20%5Cpi%20rh%2B2%20%5Cpi%20r%5E%7B2%7D%20%5C%5C%0ASA%20%3D%202%20%5Cpi%20%282.5%29%284%29%2B2%20%5Cpi%20%282.5%29%5E%7B2%7D%5C%5C%0ASA%20%5Capprox%20102.1%20%5C%3A%20in%5E%7B2%7D%20)
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The surface area is about 102.1 square inches.</span>