Question

surface area of cylinders practice
complete this assessment to review what youve learned. it will not count toward your gr
what is the formula for the total surface area of a cylinder? (1 point)

Explanation:

Step1: Analyze 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 \(A = \pi r^{2}\), and for two bases, it's \(2\pi r^{2}\).
The lateral surface area of a cylinder (when un - rolled, it's a rectangle with height \(h\) and length equal to the circumference of the base \(C = 2\pi r\)) is \(A_{lateral}=2\pi r h\).

Step2: Combine the areas of the bases and the lateral surface

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

Answer:

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