Bottle - volume

vCalc Reviewed

$V = 1/3 * pi * "h2" ( "a" ^2+ "a" * "b" + "b" ^2) + pi * "b" ^2 * "h1"$

$(a) "Neck Radius"$

$(h2)"Neck Height"$

$(b) "Base Radius"$

$(h1)"Base Height"$

The Math / Science

Geometrically, a bottle shaped object is the combination of right circular cone with a frustum defined by base radius (a) and top radius (b) and height (h₂) in between and a cylinder of radius (b) and height (h₁). See diagram.

The formula for the volume of a bottle is:

$V = (pi/3)*h2*(a^2+a*b+b^2) + pi * b^2 * h1$

where:

V = volume of the bottle
h1 = height of cone
h2 = height of cylinder
b = radius of base and bottom of cone
a = radius of top of cone

Bottle Calculators

Surface Area of a Bottle: This computes the surface area of a bottle shaped object based on the dimensions.
Mass of the Contents of a Bottle: This computes the weight or mass of a bottle shaped object based on the dimensions and the density of its contents.
Volume of a Bottle: This computes the volume of a bottle shaped object based on the dimensions.
Bottle Coating Amount: This computes the volume of material needed to coat the surface area of a bottle shaped object.

Volume is a three dimensional measurement of the amount of space taken up by an object. Volume units are cubic measurements for solid objects such as cubic inches and cubic meters. Fluids have separate volume units such as liters, fluid ounces, cups, gallons, and barrel.

The volume of an object can measured by the liquid it displaces or be calculated by measuring its dimensions and applying those dimensions to a formula describing its shape. Many such calculations are available in the following list of calculators.

In many cases, the calculators are for a column with a geometric shaped base and vertical sides. One basic formula for volume is area times a Height when the volume has vertical sides.

Bottle - volume

The Math / Science

Bottle Calculators

Volume Calculators