Question

surface area of cylinders practice
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what is the formula for the total surface area of a cylinder? (1 point)
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Explanation:

Step1: Recall the components of a cylinder's surface area

A cylinder has two circular bases and a lateral (curved) surface.
The area of a circle is \(A_{base}=\pi r^{2}\), and there are two bases, so \(A_{bases} = 2\pi r^{2}\).
The lateral surface area of a cylinder (when un - rolled, it is a rectangle with height \(h\) and length equal to the circumference of the base \(C = 2\pi r\)), so \(A_{lateral}=2\pi r h\).

Step2: Sum up the areas of the components

The total surface area \(A\) of a cylinder is the sum of the areas of the two bases and the lateral surface area.
\(A=2\pi r^{2}+2\pi r h\), which can be factored as \(A = 2\pi r(r + h)\)

Answer:

The formula for the total surface area of a cylinder is \(A=2\pi r^{2}+2\pi r h\) (or \(A = 2\pi r(r + h)\))