mathematics & mensuration

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MATHEMATICS Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions“. Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

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Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered.



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In the broadest sense, mensuration is all about the process of measurement. Mensuration is based on the use of algebraic equations and geometric calculations to provide measurement data regarding the width, depth and volume of a given object or group of objects. While the measurement results obtained by the use of mensuration are estimates rather than actual physical measurements, the calculations are usually considered very accurate.

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Mensuration is often based on making use of a model or base object that serves as the standard for making the calculations. From that point, advanced mathematics is employed to project measurements of length, width, and weight associated with like items. The end result is data that can help to make the best use of resources available today while still planning responsibly for the future.

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In general, the utilization of the principles of algebra and geometry in the measuring process are capable of providing reliable data that is based on the existence of a specified set of factors. However, it is important to note that mensuration is not the only approach that is used to project future growth and volume. Because there is always the chance for unexpected elements to enter the process, the measurements obtained from the process of mensuration are normally considered a baseline. Predictions of future patterns that do factor in acts of nature and other volatile factors are then created using the results of the mensuration process as the foundation rather than the sole projection of the ultimate outcome.

Surface area and volume:

Surface area and volume Surface Area - It is the sum of areas of all visible (exposed) surfaces of a solid. Volume - It is the three dimentional space occupied by a solid, liquid or gas.

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1.Cuboid - It is a solid figure bonded by 6 faces each of which is a rectangle, opposite rectangles being equal in length and breadth Surface Area of Cuboid or Rectangular Prism = 2( lb+bh+lh ) where l is length, b is breadth or width, h is height lateral Surface Area of Cuboid or Rectangular Prism = 2h( l+b ) Volume of Cuboid or Rectangular Prism = length×breadth×height 2.Cube - It is a solid figure bonded by 6 faces each of which is a square

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3. Cylinder- lateral Surface Area of Cylinder = 2(Pi) r × h Whole Surface Area of Cylinder = 2(Pi) × h+2 (Pi) r^2 where r is radius and h is height of cylinder 4. Cone - It is the solid figure bounded by a plane base and the     surface (called the lateral surface) formed by the locus of all straight line segments joining the vertex to the boundary of the base. lateral Surface Area of Cone = (Pi) × r × l Whole Surface Area of Cone = (Pi) × r × l + (Pi) r^2 where r is radius and l is slant height of cone

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5. Sphere -a sphere is the locus of all points in three-dimensional space which are at constant distance  from a fixed point of that space, where constant distance is radius Surface Area of sphere = 4 (Pi) radius^2 6. Hemisphere - half of the sphere (a sphere cut by a plane passing through the centre) lateral Surface Area of hemi sphere = 2 (Pi) radius^2 Whole Surface Area of hemi sphere = 3 (Pi) radius^2



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