Missing Height From Cylinder Volume

Missing Height from Cylinder Volume

A cylinder’s volume is found with

[V=\pi r^2 h]

If the height is missing, treat it as the unknown and solve for (h).

1) Identify the given values

• Write down the volume (V).
• Write down the radius (r). If the diameter is given, divide by 2 first.

2) Substitute into the formula

Replace (V) and (r) in

[V=\pi r^2 h]

This gives an equation with only one unknown, (h).

3) Isolate the height

Divide both sides by (\pi r^2):

[h=\frac{V}{\pi r^2}]

Then simplify the fraction or exact expression as much as possible. If the answer should stay exact, keep (\pi) in the denominator or numerator as needed.

4) Check your work

Multiply your height back by (\pi r^2). The result should match the original volume.

Common mistakes

• Using diameter instead of radius.
• Forgetting to square the radius.
• Rounding too early instead of simplifying first.

The key idea is to reverse the volume formula by dividing by the base area (\pi r^2).