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A class that contains one or more abstract methods must also be declared as abstract by preceding its class declaration with the abstract specifier Since an abstract class does not define a complete implementation, there can be no objects of an abstract class Thus, attempting to create an object of an abstract class by using new will result in a compile-time error When a derived class inherits an abstract class, it must implement all of the abstract methods in the base class If it doesn t, then the derived class must also be specified as abstract Thus, the abstract attribute is inherited until such time as a complete implementation is achieved Using an abstract class, you can improve the TwoDShape class Since there is no meaningful concept of area for an undefined two-dimensional figure, the following version of the preceding program declares Area( ) as abstract inside TwoDShape and TwoDShape as abstract This, of course, means that all classes derived from TwoDShape must override Area( )

// Create an abstract class using System; abstract class TwoDShape { double pri_width; double pri_height; // A default constructor public TwoDShape() { Width = Height = 00; name = "null"; } // Parameterized constructor public TwoDShape(double w, double h, string n) { Width = w; Height = h; name = n; } // Construct object with equal width and height public TwoDShape(double x, string n) { Width = Height = x; name = n; } // Construct a copy of a TwoDShape object public TwoDShape(TwoDShape ob) { Width = obWidth; Height = obHeight; name = obname; } // Properties for Width and Height public double Width { get { return pri_width; } set { pri_width = value < 0 -value : value; } }

When the planar is rotated about the x axis, it will generate a donut-shaped solid Notice that the curves intersect at x = 1 and x = 3; hence the intersection lies over the interval [ 1, 3] For each x in that interval, the segment connecting ( x, x 2 + 1) to ( x, 2x + 4) will be rotated about the x-axis It will generate a washer See Figure 818 The area of that washer is A( x) = [2x + 4]2 [x 2 + 1] [Notice that we calculate the area of a washer by subtracting the areas of two circles---not by subtracting the radii and then squaring] It follows that the volume of the solid generated is

Punctuate to ensure that your meaning is clear Inserting punctuation marks consistently helps your reader understand your intent There are several rules, but many punctuation issues are a matter of opinion or style: There is more than one acceptable alternative By deciding how you ll handle these style dilemmas once and for all, you ll save time and ensure clarity Once you know which rules you need to follow, you are in a good position to make decisions that suit you and to apply them consistently In this section, we ll discuss the fth question, How has comma usage changed since I left school , as well as clarify other punctuation issues that frequently arise in business writing

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public double Height { get { return pri_height; } set { pri_height = value < 0 -value : value; } } public string name { get; set; } public void ShowDim() { ConsoleWriteLine("Width and height are " + Width + " and " + Height); } // Now, Area() is abstract public abstract double Area(); } // A derived class of TwoDShape for triangles class Triangle : TwoDShape { string Style; // A default constructor public Triangle() { Style = "null"; } // Constructor for Triangle public Triangle(string s, double w, double h) : base(w, h, "triangle") { Style = s; } // Construct an isosceles triangle public Triangle(double x) : base(x, "triangle") { Style = "isosceles"; } // Construct a copy of a Triangle object public Triangle(Triangle ob) : base(ob) { Style = obStyle; } // Override Area() for Triangle public override double Area() { return Width * Height / 2; } // Display a triangle's style public void ShowStyle() { ConsoleWriteLine("Triangle is " + Style); } } // A derived class of TwoDShape for rectangles class Rectangle : TwoDShape {

Part I: