Volume Of A Partially Filled Cylinder - Math Open Reference

Math Open Reference Home Contact About Subject Index Volume of a partially filled cylinder Definition: A shape formed when a cylinder is cut by a plane parallel to the sides of the cylinder. Try this Drag the orange dots, note how the volume changes. See also: Volume of a cylinder

If we take a horizontal cylinder, and cut it into two pieces using a cut parallel to the sides of the cylinder, we get two horizontal cylinder segments. In the figure above, the bottom one is shown colored blue. The other one is the transparent part on top.

If we look a the end of the cylinder, we see it is a circle cut into two circle segments. See Circle segment definition for more.

Whenever we have a solid whose cross-section is the same along its length, we can always find its volume by multiplying the area of the end by its length. So in this case, the volume of the cylinder segment is the area of the circle segment, times the length.

So as a formula the volume of a horizontal cylindrical segment is Where s = the area of the circle segment forming the end of the solid, and l = the length of the cylinder.

The area of the circle segment can be found using it's height and the radius of the circle. See Area of a circle segment given height and radius.

Calculator

Use the calculator below to calculate the volume of a horizontal cylinder segment. It has been set up for the practical case where you are trying to find the volume of liquid is a cylindrical tank by measuring the depth of the liquid.

For convenience, it converts the volume into liquid measures like gallons and liters if you select the desired units. If you do not specify units the volume will be in whatever units you used to input the dimensions. For example, if you used feet, then the volume will be in cubic feet. Use the same units for all three inputs.

Units	None Metric US
Cylinder diameter
Cylinder length
Depth
Volume
Calculate Clear

As a formula

volume = where: R is the radius of the cylinder. D is the depth. L is the length of the cylinder

Notes:

• The result of the cos-1 function in the formula is in radians.
• The formula uses the radius of the cylinder. This is half its diameter.
• All inputs must be in the same units. The result will be in those cubic units. So for example if the inputs are in inches, the result will be in cubic inches. If necessary the result must be converted to liquid volume units such as gallons.

Related topics

• Definition of a face
• Definition of an edge
• Volume

• Definition and properties of a cube
• Volume enclosed by a cube
• Surface area of a cube

• Definition and properties of a pyramid
• Oblique and right pyramids
• Volume of a pyramid
• Surface area of a pyramid

• Cylinder - definition and properties
• Cylinder relation to a prism
• Cylinder as the locus of a line
• Oblique cylinders
• Volume of a cylinder
• Volume of a partially filledcylinder
• Surface area of a cylinder

• Prism definition
• Volume of a prism
• Surface area of a prism

• Volume of a sphere
• Surface area of a sphere

• Definition of a cone
• Oblique and Right Cones
• Volume of a cone
• Surface area of a cone
• Derivation of the cone area formula
• Slant height of a cone

• Conic sections - the circle
• Conic sections - the ellipse

• Icosahedron (20 faces each an equilateral triangle)

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