Cylinder, Cone and Sphere Volume: Compare Like for Like

Choose what stays the same

A cone is one-third of a cylinder only when both have the same base radius and perpendicular height. A sphere has no independently selectable height: its full height is its diameter, 2r. Comparisons become misleading when the radius or height silently changes.

Use this guide when comparing ideal container shapes or checking a geometry answer. For the basic measurements and all five supported solids, start with the volume formula guide. The Volume Calculator evaluates one solid at a time; the comparisons below show which inputs to hold fixed.

Same radius and the same overall height

Let each solid have radius r. Set the cylinder and cone height to 2r so that they are as tall as the sphere. Then:

• Cylinder: V = πr²(2r) = 2πr³.
• Sphere: V = 4πr³/3.
• Cone: V = πr²(2r)/3 = 2πr³/3.

Cylinder : sphere : cone = 3 : 2 : 1, when radius is shared and cylinder/cone height is 2r.

For r = 3 cm, the diameter is 6 cm. Enter radius 3 and height 6 for the cylinder and cone, and radius 3 for the sphere.

The sphere occupies two-thirds of its enclosing cylinder's ideal volume; the empty space is 18π cm³, or 56.55 cm³. These are volume ratios, not a claim that a solid sphere and cone physically fit together to fill that cylinder.

Same radius and same volume: height must change

If the cylinder has radius 3 cm and height 6 cm, a cone of radius 3 cm needs height 18 cm to match its 54π cm³ volume. A cone must be three times as tall to compensate for its one-third factor when the base stays fixed.

To match a sphere of radius r instead, solve πr²h = 4πr³/3 for a cylinder: h = 4r/3. For a cone, solve πr²h/3 = 4πr³/3: h = 4r. With r = 3 cm, a cylinder of height 4 cm and a cone of height 12 cm each have volume 36π cm³, matching the sphere's 113.10 cm³.

These alternatives cannot simultaneously keep the same radius, height and volume. Decide which measurement is constrained before choosing a container or checking an answer.

Radius, diameter and scaling mistakes

If a drawing gives diameter 6 cm, enter radius 3 cm. Entering 6 as the radius makes a cylinder or cone four times too large when height stays fixed, and makes a sphere eight times too large. That follows directly from the squared and cubed radius terms.

Doubling every linear dimension multiplies every solid's volume by eight. Doubling only a cylinder's height doubles its volume. Doubling only its radius quadruples volume. The phrase “twice as big” is therefore too vague for a capacity comparison.

Capacity checks and limits

For usable internal capacity, use internal dimensions in one unit throughout. The calculator's unit selector labels those dimensions; it does not convert numbers already entered. A shape with volume 169.65 cm³ has ideal capacity about 0.16965 L because 1,000 cm³ = 1 L. Do not round each dimension or π before the final step.

Wall thickness, a rounded base, a truncated cone, a lid and space left for filling can change real capacity. A full sphere formula also does not give the volume of a partly filled spherical tank. Measure the actual geometry rather than treating these ideal formulas as a guaranteed usable capacity.

Quick comparison checks

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