Interpolation Definition In the mathematical sub field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. Linear interpolation is a method of curve fitting using linear polynomials. It is heavily employed in mathematics (particularly numerical analysis), and numerous applications including computer graphics. It is a simple form of interpolation. Many times, while making the graphs of functions in experimental science and statistical mathematics, we get such complex functions whose real set of coordinate points are difficult to obtain and plot on a graph. In such cases, we use the method of interpolation, and plot the graph of a simple function that has the closest graph to the original complex function. Although the graph of such a function is not accurate, the small error encountered by interpolation is negligible to the simplicity obtained in making complex graphs by interpolation. Know More About Dividing Polynomials Worksheet
Linear Interpolation: The term "linear" in mathematics implies an equation whose degree is one. Thus, "linear interpolation" is the method of interpolation with linear functions and their graphs. Thus linear interpolation is the simplest type of interpolation. Definition of Linear Interpolation The linear interpolation is the straight line between the two points which are given by the coordinates (x0, y0) and (x1, y1). In the interval of (x0, x1) the value of x which gives the straight line and it is given from the equation for the value of y along. y−y0x−x0 = y1−y0x1−x0 It can be derived geometrically as follow, Solve the above for the unknown value of y y = y0 + (x- x0) y1−y0x1−x0 In the interval (x0, x1), it is the linear interpolation formula. Example Problem for Linear Interpolation Formula Some example problem for linear interpolation formula are, Learn More Fact Family Worksheet
Example 1: Using linear interpolation formula, for the given coordinates of (1, 2) and (4, 5). Find the value for y when x = 2 Solution: Linear interpolation formula y = y0 + (x- x0)y1−y0x1−x0 Given coordinate values are (1, 2) and (4, 5) (x0, y0) and (x1, y1) are (x0, y0) and (x1, y1). y = 2 +(x - 1) (5−2)(4−1) y = 2 + x -1 33 y = 2 + x - 1(1) y = x + 1. Value of y when x = 2. y=x+1 x=2 y = 2 +1
Total Surface Area of a Cylinder A Cylinder has a circular base. It can be of the shape of a pillar, a rubber tube, the trunk of a tree, etc. The term 'circular cylinder' is commonly used to describe aright circular cylinder. A right circular cylinder is a circular cylinder that has perpendicular base and height. The diagram shown below is of a right circular cylinder. In the above diagram, h = height of the circular cylinder r = radius of base of circular cylinder We can also say that a circular cylinder is a rolled form ofa rectangle.The area of the rectangle that forms a cylinder is called the curvedsurface area of a cylinder, since the rectangle forms the curved surface of the cylinder.When we cut a cylinder vertically, thecross section obtained is a rectangle. In other words, when a rectangle is revolved around one of its sides, a cylinder is obtained
When we add the area of the top and bottom circles of a cylinder to its curved surface area, we get theTotal surface area of a cylinder. Curved Surface Area of a Cylinder The curced surface area of a cylinder is given by the following formula, Curved Surface Area = 2 * π * r * h, where, π = 22/7 or 3.14 r = radius of the base circles of cylinder h = height of the cylinder Total Surface Area of a Cylinder Total Surface Area = (π * r²) + (π * r²) + (2 * π * r * h), where (π * r²) = Area of the base circle (2 * π * r * h) = Area of the curved surface of cylinder Read More About Inequality Worksheets
Solved Examples on Cylinders Given below are some of the examples on Cylinder Example 1: Find the curved surface area of the cylinder with height = 15 cm and radius of base circle = 5 cm. Solution: Given, Radius, r = 5 cm Height, h = 15 cm Area of curved surface, CSA = 2 * π * r * h = 2 * 3.14 * 5 x 15 = 471 cm² Example 2: Find the Total Surface Area of a cylinder whose height is 20 meters and radius of base circle is 2 meters. Solution:
Given, Radius, r = 2 m Height, h = 20 m Total Surface Area of Cylinder, TSA = (π * r²) + (π* r²) + (2 * π * r * h) = (3.14 * 5) + (3.14 * 5) + (2 * 3.14 * 5 * 20) = 19719.2 m² Example 3: Find the Volume of a cylinder whose height = 28 cm and diameter = 12 cm Solution : Given, Diameter, d = 12 cm, therefore Radius, r = d/2 = 12/2 = 6 cm Height, h = 28 cm Volume = π * r² * h = 3.14 * 6 * 28 = 527.52 m³
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