Surface Area Formulas
In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object. Cube | Rectangular Prism | Prism | Sphere | Cylinder | Units

Note: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times "a".

Be careful!! Units count. Use the same units for all measurements. Examples

|Surface Area of a Cube = 6 a 2 |

[pic](a is the length of the side of each edge of the cube)
In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.

|Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac |

[pic](a, b, and c are the lengths of the 3 sides)
In words, the surface area of a rectangular prism is the are of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same. The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.

|Surface Area of Any Prism |

[pic] (b is the shape of the ends)
Surface Area = Lateral area + Area of two ends
(Lateral area) = (perimeter of shape b) * L
Surface Area =...

...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 crushed into powder as there is a bigger total surfacearea resulting in more effective collisions between particles.
Variables:
Independent variable: Different forms of tablets.
Dependant variable: Time the syringe took to stop moving as the tablets dissolve.
Fixed variables:
*External temperature
*volume of HCl
*Temperature –all 3 final runs were done on the same day so whether was not an issue and did not affect the results
*Use of catalyst – a catalyst was not used in any of the experiments
* Use the same person to observe the reaction because different people have different eyesight
Background information relating to the experiment
In this experiment we are looking at one effect that influences the rate of reaction , namely total surfacearea. The reaction rate (rate of reaction) or speed of reaction for a reactant or product in a particular reaction is defined as how fast or slow a reaction takes place....

...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 would take too long for the nutrients and oxygen to diffuse into the cell so the cell would probably not survive. Single celled organisms can survive as they have a large enough surfacearea to allow all the oxygen and nutrients they need to diffuse through. Larger multi celled organisms need specialist organs to respire such as lungs or gills.
Apparatus Needed For the Experiments:
1. Beakers
2. Gelatin blocks mixed containing universal indicator
3. 0.1M Hydrochloric acid
4. Stop Watch
5. Scalpel
6. Tile
7. Safety glasses
Method:
1. A block of gelatin which has been dyed with universal indicator should be cut into blocks of the following sizes (mm).
5 x 5 x 5
10 x 10 x 10
15 x 15 x 15
20 x 20 x 20
10 x 10 x 2
10 x 10 x 10 (Triangle)
10 x 15 x 5
20 x 5 x 5
The triangle is of the following dimensions.
The rest of the blocks are just plain cubes or rectangular blocks.
Universal indicator is a neutral indicator....

...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. 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 would take too long for the nutrients and oxygen to diffuse into the cell so the cell would probably not survive.
Single celled organisms can survive as they have a large enough surfacearea to allow all the oxygen and nutrients they need to diffuse through. Larger multi-celled organisms need organs to respire such as lungs or gills.
Method
The reason I chose to do this particular experiment is because I found it very interesting and also because the aim, method, results- basically the whole experiment would be easily understood by the average person who knew nothing about SurfaceArea/Volume Ratio. The variable being tested in this experiment is the rate of diffusion in relation to the size of the gelatin...

...AREA
(i) The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively. If one of the diagonal of the rhombus is 22 cm, find the length of the other diagonal.
(ii) The floor of a rectangular hall has a perimeter 250m. If the cost of paining the four walls at the rate of Rs 10 per m2 is Rs 1500. Find the height of the hall.
(iii) A room is half as long again as it is broad. The cost of carpeting the room at Rs 3.25 per m2 is Rs 175.50 and the cost of papering the walls at Rs 1.40 per m2 is Rs 240.80. If 1 door and 2 windows occupy 8m2, find the dimensions of the room.
(iv) A river 2m deep and 45m wide is flowing at the rate of 3 km per hour. Find the volume of water that runs into the sea per minute.
(v) A closed cylinder has diameter 8cm and height 10cm. Find its total surfacearea and volume.
(vi) The volume of a metallic cylinder pipe is 748cm3 . Its length is 14 cm and external diameter 18cm. Find its thickness.
(vii) A cylindrical bucket, 28cm in diameter 72cm high is full of water. The water is emptied into a rectangular tank, 66cm long and 28cm wide. Find the height of the water level in the tank.
(viii) A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4cm and its length is 25cm. The thickness of the metal is 8mm...

...Kimberly M Dollar
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 what it means to find the surfacearea. The surfacearea is not the same as finding the volume of a cube. The surfacearea is the area on the outside of a three-dimensional shape, like the cube. The surfacearea of a cube is six times the surfacearea of one side of the cube. There are six sides to one cube, after learning this about a cube the appropriate formula to find the surfacearea is:
Surfacearea of a cube=6s^2 (The “6” represents the number of sides; “s” represents one side of a cube; “^2” represents taking one side and timing it by itself; the end result gives the surfacearea of a cube).
Prerequisite Skills
The necessary prerequisite skills required to determine the surfacearea...

...w
The Effect 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 rate of reaction. Therefore, my hypothesis is that when the surfacearea increases the rate of reaction increases.
Background information:
“Collision theory is a theory proposed independently by Max Trautzin 1916 and William Lewis in 1918, that qualitatively explains how chemical reactions occur and why reaction rates differ for different reactions. The collision theory states that when suitable particles of the reactant hit each other, only a certain percentage of the collisions cause any noticeable or significant chemical change; these successful changes are called successful collisions. The successful collisions have enough energy, also known as activation energy, at the moment of impact to break the pre-existing bonds and form all new bonds. This results in the products of the reaction. Increasing the concentration of the reactant particles or raising the temperature, thus bringing about more collisions and therefore many more...

...SurfaceareaSurfacearea is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surfacearea is considerably more involved than the definition of arc length of a curve. For polyhedra (objects with flat polygonal faces) the surfacearea is the sum of the areas of its faces. Smoothsurfaces, such as a sphere, are assigned surfacearea using their representation as parametric surfaces. This definition of the surfacearea is based on methods of infinitesimal calculus and involves partial derivatives and double integration.
General definition of surfacearea 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 surfacearea for irregular objects of any dimension. An important example is the Minkowski content of a surface.
Definition of surfacearea
While areas of many simple surfaces have been known since antiquity, a rigorous mathematical definition of area requires a lot of care. Surfacearea...

...| |Subject: Surfacearea of a sphere |
A connection which could be illustrated, and could be understood by students who know the perimeter of a circle, runs as follows:
Put the sphere of radius R inside a cylinder, with the cylinder just touching the equator, and cut off at the height of the top and bottom of the sphere. (A cutaway view is in the diagram.)
[pic]
What is the area of the curved part of the cylinder? 2 Pi R x 2R = 4 Pi R2. This is found by slicing the cylinder surface and rolling it out as a rectangle.
Now, it is NOT an accident that the cylinder surface is EXACTLY the area of the sphere.
Take in small horizontal slice through the diagram. (I have colored one such slice orange.) This cuts a rectangle out of the rolled out cylinder and slightly distorted rectangle out of the sphere. (If the slice is very thin then the distortion is "slight".)
In the cross-sectional view below hc is the height of the slice on the cylinder, hs is the length of the arc on the sphere cut out by the slice, r is the radius of the distorted rectangle on the sphere and R is the radius of the sphere.
[pic]
The area of the orange rectangle on the cylinder is 2 Pi R hc and the area of the distorted orange rectangle on the sphere is approximately 2 Pi r hs. These...