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# Where does the surface area formula come from?

## Where does the surface area formula come from?

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

What is the history of surface area?

A 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.

### Who found surface area and volume?

Archimedes
A spectacular landmark in the history of mathematics was the discovery by Archimedes (287-212 B.C.) that the volume of a solid sphere is two- thirds the volume of the smallest cylinder that surrounds it, and that the surface area of the sphere is also two-thirds the total surface area of the same cylinder.

What is surface area in mathematics?

The total area of the surface of a three-dimensional object. Example: the surface area of a cube is the area of all 6 faces added together. See: Area.

## How do u get the surface area?

Multiply the length and width, or c and b to find their area. Multiply this measurement by two to account for both sides. Add the three separate measurements together. Because surface area is the total area of all of the faces of an object, the final step is to add all of the individually calculated areas together.

How is the surface area of a cube derived?

The formula for surface area is equal to six times of square of length of the sides of cube. It is represented by 6a2, where a is the side length of cube.It is basically the total surface area.

### Who invented area?

In the 7th century CE, Brahmagupta developed a formula, now known as Brahmagupta’s formula, for the area of a cyclic quadrilateral (a quadrilateral inscribed in a circle) in terms of its sides.

Is surface area a TSA or CSA?

Curved Surface Area (CSA) – It includes the area of all the curved surfaces. Lateral Surface Area (LSA) – It includes the area of all the surface excluding the top and bottom areas. Total Surface Area (TSA) – It includes the area of all the surfaces of the object including the bases.

## What are the inventions of Archimedes?

Archimedes’ screw
ArchitonnerreClaw of Archimedes
Archimedes/Inventions

Who discovered area?

### What is the purpose of finding surface area?

The surface area of a three-dimensional object is the total area of all of its surfaces. Surface area is important to know situations where we want to wrap something, paint something, and eventually while building things to get the best possible design.

What is total surface area?

The total surface area of a solid is the sum of the areas of all of the faces or surfaces that enclose the solid. The area of the rectangle is the lateral surface area. The sum of the areas of the rectangle and the two circles is the total surface area.

## Which is the correct equation for surface area?

Surface Area = 2 ( pi r 2) + (2 pi r)* h. Tip! Don’t forget the units. These equations will give you correct answers if you keep the units straight. For example – to find the surface area of a cube with sides of 5 inches, the equation is: Surface Area = 6* (5 inches) 2.

How to calculate the surface area of a sphere?

For spheres, calculate the surface area if you know the radius r r: For hemispheres, you calculate the surface area as the sum of the base surface area, πr2 π r 2, plus the half sphere, 2πr2 2 π r 2, which gives: For cones with slant height l l and radius r r, surface area is calculated using this formula:

### How do you calculate the surface area of a can?

Surface Area = Areas of top and bottom +Area of the side Surface Area = 2 (Area of top) + (perimeter of top)* height Surface Area = 2 (pi r 2) + (2 pi r)* h In words, the easiest way is to think of a can.

How to find the surface area of a plane?

Example 1 Find the surface area of the part of the plane 3x +2y+z =6 3 x + 2 y + z = 6 that lies in the first octant. Remember that the first octant is the portion of the xyz -axis system in which all three variables are positive. Let’s first get a sketch of the part of the plane that we are interested in.