Surface Area of a Cylinder Math Example 4

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

Example 4

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 π\pi.

Solution

  1. 1
    Step 1: The lateral surface area of a cylinder is 2πrh2\pi rh (the curved side, excluding the circular bases).
  2. 2
    Step 2: LSA=2π(3)(7)=42πLSA = 2\pi(3)(7) = 42\pi cm².

Answer

Lateral surface area =42π= 42\pi cm².
The lateral surface area is just the curved rectangular side of the cylinder. When unrolled flat, it is a rectangle with length equal to the circumference (2πr2\pi r) and width equal to the height (hh). This is useful for problems like painting just the sides of a can.

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 1 easy

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

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 5 hard

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

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