Surface Area of a Cylinder Math Example 5

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

hard

A cylinder's height equals its diameter. If the total surface area is

108\pi

cm², find the radius.

1
Step 1: Let radius $= r$ . Since height equals diameter: $h = 2r$ .
2
Step 2: Substitute into $SA = 2\pi r^2 + 2\pi rh$ : $108\pi = 2\pi r^2 + 2\pi r(2r) = 2\pi r^2 + 4\pi r^2 = 6\pi r^2$ .
3
Step 3: Divide both sides by $6\pi$ : $r^2 = 18$ .
4
Step 4: $r = \sqrt{18} = 3\sqrt{2} \approx 4.24$ cm.

Answer

r = 3\sqrt{2} \approx 4.24

cm.

Introducing the constraint

h = 2r

reduces the problem from two unknowns to one. After substitution, the surface area formula simplifies to

6\pi r^2

, which can be solved directly for

r

. This type of problem involves recognizing and using geometric constraints.

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.

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