To find the volume of a cylinder , you use this formula:

V=πr2hV=\pi r^2hV=πr2h

where rrr is the radius of the circular base and hhh is the height of the cylinder.

Quick Scoop

1. The basic formula

  • Volume of a cylinder: V=πr2h;V=\pi r^2hV=πr2h.
  • rrr = radius of the base (half the diameter).
  • hhh = height of the cylinder (distance between the two circular bases).
  • π≈3.14\pi \approx 3.14π≈3.14 is the same constant you use for circles.

Think of it as:

Area of the circle at the bottom × height of the cylinder.

Because the area of a circle is πr2\pi r^2πr2, stacking that area up through height hhh gives πr2h\pi r^2hπr2h.

2. Step‑by‑step method (normal cylinder)

  1. Identify the radius and height.
    • Make sure they are in the same units (both in cm, both in m, etc.).
  1. Square the radius.
    • Compute r2r^2r2 (multiply the radius by itself).
  1. Multiply by π\pi π.
    • Do πr2\pi r^2πr2 to get the base area.
  1. Multiply by the height.
    • Now do πr2h\pi r^2hπr2h to get the volume.
  1. Write the units as cubic units (like cm³, m³, in³).

3. Example you can copy

Example: A cylinder has radius 5 cm and height 10 cm. Find its volume.

  1. Radius r=5r=5r=5 cm, height h=10h=10h=10 cm.
  2. r2=52=25r^2=5^2=25r2=52=25.
  3. Base area =πr2≈3.14×25=78.5=\pi r^2\approx 3.14\times 25=78.5=πr2≈3.14×25=78.5 cm².
  1. Volume V=πr2h≈3.14×25×10=785V=\pi r^2h\approx 3.14\times 25\times 10=785V=πr2h≈3.14×25×10=785 cm³.

So the volume is about 785 cm³.

4. If you’re given diameter instead of radius

Sometimes problems give you the diameter ddd of the cylinder’s base.

  • Radius is half the diameter : r=d2r=\dfrac{d}{2}r=2d​.
  • Plug into the formula, you can rewrite it as:

V=πd2h4V=\frac{\pi d^2h}{4}V=4πd2h​

This is just the same formula written using ddd instead of rrr.

5. If you’re given circumference instead of radius

If you know the circumference CCC of the base and the height:

  • Circumference of a circle: C=2πrC=2\pi rC=2πr.
  • Solve for rrr: r=C2πr=\dfrac{C}{2\pi}r=2πC​.
  • Then still use V=πr2hV=\pi r^2hV=πr2h after finding rrr.

6. Special types (just in case)

You might see variations in harder problems:

  • Slanted (oblique) cylinder : Surprisingly, the volume is still base area × vertical height , just like a straight cylinder, as long as you use the true vertical height.
  • Oval (elliptic) cylinder : Base is an ellipse; find the area of the ellipse first, then multiply by height.

For school-level questions about “how to find volume of a cylinder,” they almost always mean the normal right circular cylinder with radius rrr and height hhh.

7. Mini FAQ

  • What are the units of volume?
    Always cubic: cm³, m³, in³, etc.
  • What happens if the radius doubles?
    Since volume goes with r2r^2r2, doubling rrr makes volume four times bigger (if height stays the same).
  • Real‑life example:
    A water bottle or a soup can is basically a cylinder; the formula tells you how much liquid it can hold.

Short TL;DR

  • Remember this line:

Circle area (πr²) × height (h) = volume of a cylinder.

Information gathered from public forums or data available on the internet and portrayed here.