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Related Concept Videos

Theorems of Pappus and Guldinus01:10

Theorems of Pappus and Guldinus

The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any body of revolution. This is done by revolving a plane curve around an axis that does not intersect the curve to find its surface area or revolving a plane area around a non-intersecting axis to calculate its volume.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...
Area Problem01:26

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Determining the area of a region with straight edges is straightforward, as geometric formulas for rectangles, triangles, and polygons can be applied directly. However, traditional geometric methods are insufficient when a region has a curved boundary, such as the area under a function.fromThe area problem involves finding a systematic way to measure such regions. One approach to solving this problem is through approximation. Instead of attempting to compute the area exactly at the outset, the...
Area of a Surface of Revolution01:29

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Surfaces of revolution are formed when a two-dimensional curve is rotated around an axis, producing a three-dimensional shape. This concept is used in engineering tasks like determining the surface area of a rocket nozzle, where precise calculations are critical for applying uniform heat-resistant coatings. When a curve is revolved about the x-axis, it sweeps out a continuous surface whose area must be calculated accurately to estimate material requirements.Approximating with Conical BandsTo...
Surface Area Calculations01:22

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Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...
Surface Integrals01:28

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A curved roof has a surface area that is generally larger than its flat projection. To estimate the cost of painting it, the curved surface area must first be calculated. If the roof is represented parametrically by a vector-valued function r(u,v), then each point in a parameter domain D corresponds to a point on the surface S. This connection allows the curved surface to be studied through a two-dimensional parameter region.The parameter domain D is divided into many small rectangles. A...

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Related Experiment Video

Updated: Jun 29, 2026

A Standardized Method for Measuring Internal Lung Surface Area via Mouse Pneumonectomy and Prosthesis Implantation
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Published on: July 26, 2017

Human body surface area: a theoretical approach.

Jianfeng Wang1, Eiji Hihara

  • 1Institute of Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, 113-0033 Tokyo, Japan. jfwang@k.u-tokyo.ac.jp

European Journal of Applied Physiology
|November 25, 2003
PubMed
Summary
This summary is machine-generated.

This study derives a new formula for calculating human body surface area (BSA) based on body mass and height. The formula, derived from geometric principles, offers accurate BSA estimations for both children and adults.

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Area of Science:

  • Biophysics
  • Anthropometry
  • Geometric modeling

Background:

  • Accurate human body surface area (BSA) estimation is crucial for medical and engineering applications.
  • Existing BSA formulas vary, necessitating a more universally applicable and theoretically grounded equation.

Purpose of the Study:

  • To derive a novel theoretical equation for human body surface area (BSA) based on fundamental geometric principles.
  • To validate the derived equation against existing BSA calculation methods across a wide age range.

Main Methods:

  • Developed a theoretical model assuming the human body as a deformed cylinder.
  • Derived an equation for BSA by minimizing surface area at a fixed volume.
  • Validated the equation using body mass (BM) and body height (BH) with an assumed density of 1,000 kg.m(-3).

Main Results:

  • The derived equation is BSA=(BM.BH/35.37)(0.5).
  • Calculated BSA values showed a +/-7% agreement with existing literature values.
  • The equation is effective for BSA estimation in children and adults.

Conclusions:

  • The new BSA equation provides a geometrically derived and accurate method for estimation.
  • The formula suggests an underlying relationship between geometric constraints and human body growth.
  • This theoretical approach offers a fundamental insight into human body surface area calculations.