Surface area
Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of the surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration. General definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.

Definition of surface area

While areas of many simple surfaces have been known since antiquity, a rigorous mathematical definition of area requires a lot of care. Surface area is an assignment of a positive real number to a certain class of surfaces that satisfies several natural requirements. The most fundamental property of the surface area is its additivity: the area of the whole is the sum of the areas of the parts. More rigorously, if a surface S is a union of finitely many pieces S1, …, Sr which do not overlap except at their boundaries then

Surface areas of flat polygonal shapes must agree with their geometrically defined area. Since surface area is a geometric notion, areas of congruent surfaces must be the same and area must depend only on the shape of the surface, but not on its position and orientation in space. This means that surface area is invariant under the group of Euclidean motions. These properties uniquely characterize surface area for a wide class of geometric surfaces called piecewise smooth. Such surfaces consist of finitely...

...Planning
Aim
To determine how the surfacearea of the tablets affects the rate of the reaction. To determine which form of tablets gives the biggest surfacearea resulting in the fastest reaction rate.
Investigation question:
What is the relationship between the total surfacearea of the tablets and the rate of the reaction?
Hypothesis:
The rate of reaction will be the fastest when the tablets...

...Surfacearea / Volume ratio Experiment
Introduction:
The surfacearea to volume ratio in living organisms is very important. Nutrients and oxygen need to diffuse through the cell membrane and into the cells. Most cells are no longer than 1mm in diameter because small cells enable nutrients and oxygen to diffuse into the cell quickly and allow waste to diffuse out of the cell quickly. If the cells were any bigger than this then it...

...INTERNATIONAL BACCALAUREATE
BIOLOGY INTERNAL ASSESMENT
DATA COLLECTION AND PROCESSING
CONCLUSION AND EVALUATION
RELATIONSHIP BETWEEN SURFACEAREA AND THE VOLUME OF A CELL, HOW IT AFFECTS THE RATE OF DIFFUSION
Nazirul Ibrahim
04.10.2011
DATA COLLECTION AND PROCESSING
We have determined the following variables:
* dV- the time for the color indicator phenolphthalein to reach the center of the cube (diffusion)
* iV- the size of the cube...

...diffusion. Diffusion is the process that cells use to obtain oxygen, water and food. Also, how they lose waste substances, for example, urea and carbon dioxide. Basically, Diffusion is when particles move from an area of high concentration to an area of low concentration. The surfacearea to volume ratio of the cell is an important factor in diffusion. It is the effect of this factor that will be investigated in this practical....

...SurfaceArea to Volume Ratio and the Relation to the Rate of Diffusion
Aim and Background
This is an experiment to examine how the SurfaceArea / Volume Ratio affects the rate of diffusion and how this relates to the size and shape of living organisms.
The surfacearea to volume ratio in living organisms is very important. Nutrients and oxygen need to diffuse through the cell membrane and into the cells....

...000234333
EFT4: Math: Task 5: SurfaceArea of Cubes
Introducing SurfaceArea
For a fifth or sixth grade class to understand the concept surfacearea in relation to a cube they need to understand what a cube is first. They will learn that a cube is a special type of rectangular solid. The length, width, and height of a cube are exactly the same. After explaining what a cube is they will need to understand...

...growth, more chemical activity will have to happen and the rate of metabolism will also increase, which means that more substances have to be taken in and to also be removed. This is where the surfacearea to volume ratio comes into place; the reason why this ratio is so important is because the surfacearea of a cell essentially affects the rate of the transferring of useful substances (through diffusion and osmosis etc.) in and out of...

...of Changing the surfacearea on the Rate of Reaction?
By :
22/10/2013
The effect of changing the surfacearea on the
rate of reaction?
Unit Question: Should we speed things up or slow them down?
Hypothesis:
According to collision theory, should the surfacearea increase the amount of collisions increase increasing the...

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