Bottle - surface area

Last modified by

on

Jul 31, 2023, 9:50:34 PM

Created by

on

Aug 21, 2014, 2:50:02 PM

A = π (a + b) \sqrt{h_{2}^{2} + {(b - a)}^{2}} + 2 \cdot π \cdot b \cdot h_{1} + π \cdot b^{2}

$A = pi( "a" + "b" ) sqrt( h_2 ^2+( "b" - "a" )^2) + 2*pi* "b" * h_1 + pi* "b" ^2$

(a) neck radius

$(a) "neck radius"$

(h 2) neck height

$(h2)"neck height"$

(b) body radius

$(b) "body radius"$

(h 1) body height

$(h1)"body height"$

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.

The Math

The formula used in this calculator is as follows:

$A = π (a + b) \sqrt{h_{2}^{2} + {(b - a)}^{2}} + 2 \cdot π \cdot b \cdot h_{1} + π \cdot b^{2}$ $A = pi(a+b) sqrt(h_2^2+(b-a)^2) + 2*pi*b*h_1 + pi*b^2$

The surface area (A) includes several geometric shapes: the tapered neck, the cylindrical body and the circular bottom. You can see this in the three components of the formula:

tapered neck (frustum of a cone): $A = π (a + b) \sqrt{h_{2}^{2} + {(b - a)}^{2}}$ $A = pi(a+b)sqrt(h_2^2 + (b-a)^2)$
cylindrical body (cylinder): $A = 2 π \cdot b \cdot h_{1}$ $A = 2pi*b*h_1$
circular bottom (circle): $A = π \cdot b^{2}$ $A=pi*b^2$

NOTES

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). The surface area is the sum of the surface of the cone frustum, the cylinder and the circle of the bottom. Note: this leave no surface area for the opening at the top.

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• Frustum by KurtHeckman

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Bottle - surface area

Bottle Calculators

The Math

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