Surface Area of a Cylinder Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Surface Area of a Cylinder.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The total area of the surface of a cylinder, consisting of two circular bases and a rectangular lateral surface that wraps around.

Imagine peeling the label off a can of soup. The label is a rectangle whose width is the circumference of the can (2\pi r) and whose height is the can's height (h). Add the two circular lids (top and bottom), and you have the total surface area.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Two circles for the top and bottom, plus a rectangle (rolled into a tube) for the side. The rectangle's width is the circumference.

Common stuck point: The lateral surface area (2\pi r h) is a rectangle whose width equals the circumference (2\pi r). Visualizing the 'unrolled' cylinder helps.

Sense of Study hint: When you see a cylinder surface area problem, break it into three parts. First, compute the area of one circular base: \pi r^2. Then double it for both bases: 2\pi r^2. Finally, add the lateral area 2\pi r h (circumference times height). The total is 2\pi r^2 + 2\pi r h.

Worked Examples

Example 1

easy
A cylinder has radius 5 cm and height 8 cm. Find its total surface area. Leave your answer in terms of \pi.

Solution

  1. 1
    Step 1: Write the formula: SA = 2\pi r^2 + 2\pi rh.
  2. 2
    Step 2: The two circular bases contribute: 2\pi r^2 = 2\pi(5)^2 = 50\pi cm².
  3. 3
    Step 3: The lateral (curved) surface contributes: 2\pi rh = 2\pi(5)(8) = 80\pi cm².
  4. 4
    Step 4: Total: SA = 50\pi + 80\pi = 130\pi cm².

Answer

SA = 130\pi cm².
The cylinder's surface area has two parts: the two circular ends (2\pi r^2) and the curved lateral surface (2\pi rh). The lateral surface, when unrolled, forms a rectangle of width 2\pi r (the circumference) and height h.

Example 2

medium
A cylindrical can has a total surface area of 150\pi cm² and a radius of 5 cm. Find the height.

Example 3

medium
Find the total surface area of a cylinder with radius 4 cm and height 10 cm.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Find the lateral surface area only (not the bases) of a cylinder with radius 3 cm and height 7 cm. Leave your answer in terms of \pi.

Example 2

hard
A cylinder's height equals its diameter. If the total surface area is 108\pi cm², find the radius.
← Back to Surface Area of a Cylinder Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

area of circlesurface areacircumference