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Area Conversion

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Important Notes
  • The SI unit of area is the square meter which is considered an SI derived unit.
  • A shape with an area of three square meters would have the same area as three such squares. In mathematics, the unit square is defined to have area one and the area of any other shape or surface is a dimensionless real number.
  • Every unit of length has a corresponding unit of area, namely the area of a square with the given side length. Thus, areas can be measured in square meters (m2), square centimeters (cm2), square millimeters (mm2), square kilometers (km2), square feet (ft2), square yards (yd2), square miles (mi2) and so forth.
  • For a solid shape such as a sphere, cone or cylinder, the area of its boundary surface is called the surface area. The surface area of a solid object is a measure of the total area that the surface of the object occupies.
  • Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra and is a basic property of surfaces in differential geometry.

Surface Area (Cube & Cuboid)

Important Notes
  • A cube has all edges the same length. This means that each of the cube's six faces is a square. The total surface area is therefore six times the area of one face, represented by the mathematical formula : the surface area A=6s2, where s is the length of any edge of the cube.
  • The lateral surface area of a cube with side length s is equal to the area of four faces : 4s2.
  • The Total surface area of a cuboid (TSA) is equal to the sum of the areas of its 6 rectangular faces, which is given by :
    TSA=2 (lb + bh + lh) square units, where l is the length, b is the breadth and h is the height of the cuboid.
  • The lateral surface area (LSA) of a cuboid is the sum of 4 planes of a rectangle, leaving the top and the base. Mathematically, it is given as: LSA=2 (lh + bh)=2 h (l + b) square units, where l is the length, b is the breadth and h is the height of the cuboid.

Surface Area (Cone & Cylinder)



Important Notes
  • A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.
  • The lateral (curved) surface area of a right circular cone is LSA=πrl , where r is the radius of the circle at the bottom of the cone and l is the slant height of the cone. The surface area of the bottom circle of a cone is the same as for any circle, πr2.
  • Therefore, the total surface area of a right circular cone is TSA=πrl + πr2=πr(r + l) .
  • A cylinder is one of the most basic curved geometric shapes, with the surface formed by the points at a fixed distance from a given line segment, known as the axis of the cylinder.
  • The lateral (curved) surface area (LSA) of a cylinder having the height h and radius r can be calculated by the mathematical formula LSA=2πrh . The total surface area of the cylinder is TSA=2πr (r+h) .

Surface Area (Sphere & Hemisphere)


Important Notes
  • A sphere is a geometrical object in three-dimensional space that is the surface of a ball. Like a circle in a two-dimensional space, a sphere is defined as the set of points that are all at the same distance r from a given point, but in a three-dimensional space.
  • The total surface area (TSA) of sphere & curved surface area (CSA) of the sphere is same and can be calculated as TSA=CSA=4πr 2 , where r is the radius of the sphere.
  • As the hemisphere is the half part of a sphere, therefore the curved surface area is also half that of the sphere. The curved surface area of hemisphere=2πr2 , where r is the radius of the hemisphere.
  • The total surface area (TSA) of a hemisphere is obtained by addition of the curved surface area and the area of the base of the hemisphere, therefore, TSA=2πr2 + πr2=3πr2 , where r is the radius of the hemisphere.
area
Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape or planar lamina, in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape or the amount of paint necessary to cover the surface with a single coat.
The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square meter (written as m2), which is the area of a square whose sides are one meter long.

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The use of units, measurements and conversions plays a big part in excelling in math. The intent of this site is to help visitors perform different varieties of calculations/conversions easily with a high degree of accuracy.

The site includes unit converters for various quantities like currency, length, speed, time, area, volume, mass, temperature, angle, pressure, energy and power. In addition to this, it provides area & volume calculations of different shapes & it's parts. The site also contains several other features like number system conversion, calculation of interests, percentages along with color code finder and many more.

History of Measurement :

The earliest recorded systems of calculations and measures originate in the 3rd or 4th millennium BC. Even the very earliest civilizations needed measurement for purposes of agriculture, construction and trade. Early standard units might only have applied to a single community or small region, with every area developing its own standards for lengths, areas, volumes and masses.

With the development of manufacturing technologies and the growing importance of trade between communities and ultimately across the Earth, standardized weights and measures became critical. Starting in the 18th century, modernized, simplified and uniform systems of weights and measures were developed, with the fundamental units defined by ever more precise methods in the science of metrology.

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