Surface Area of a Cylinder Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

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

Solution

  1. 1
    Step 1: Write the formula: SA=2πr2+2πrhSA = 2\pi r^2 + 2\pi rh.
  2. 2
    Step 2: The two circular bases contribute: 2πr2=2π(5)2=50π2\pi r^2 = 2\pi(5)^2 = 50\pi cm².
  3. 3
    Step 3: The lateral (curved) surface contributes: 2πrh=2π(5)(8)=80π2\pi rh = 2\pi(5)(8) = 80\pi cm².
  4. 4
    Step 4: Total: SA=50π+80π=130πSA = 50\pi + 80\pi = 130\pi cm².

Answer

SA=130πSA = 130\pi cm².
The cylinder's surface area has two parts: the two circular ends (2πr22\pi r^2) and the curved lateral surface (2πrh2\pi rh). The lateral surface, when unrolled, forms a rectangle of width 2πr2\pi r (the circumference) and height hh.

About Surface Area of a Cylinder

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

Learn more about Surface Area of a Cylinder →

More Surface Area of a Cylinder Examples

Example 2 medium

A cylindrical can has a total surface area of [formula] 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.

Example 4 easy

Find the lateral surface area only (not the bases) of a cylinder with radius 3 cm and height 7 cm. L

Example 5 hard

A cylinder's height equals its diameter. If the total surface area is [formula] cm², find the radius

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