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Imagine that a water tank in the shape of a hemisphere of radius 10 feet is being pumped out (Figure 826) Find the work done in lowering the water level from 1 foot from the top of the tank to 3 feet from the top of the tank

When you declare a variable inside a for loop, there is one important point to remember: The scope of that variable ends when the for statement does (That is, the scope of the variable is limited to the for loop) Outside the for loop, the variable will cease to exist Thus, in the preceding example, i is not accessible outside the for loop If you need to use the loop control variable elsewhere in your program, you will not be able to declare it inside the for loop Before moving on, you might want to experiment with your own variations on the for loop As you will find, it is a fascinating loop

As powerful and useful as inheritance is, sometimes you will want to prevent it For example, you might have a class that encapsulates the initialization sequence of some specialized hardware device, such as a medical monitor In this case, you don t want users of your class to be able to change the way the monitor is initialized, possibly setting the device incorrectly Whatever the reason, in C# it is easy to prevent a class from being inherited by using the keyword sealed To prevent a class from being inherited, precede its declaration with sealed As you might expect, it is illegal to declare a class as both abstract and sealed because an abstract class is incomplete by itself and relies upon its derived classes to provide complete implementations Here is an example of a sealed class:

sealed class A { // } // The following class is illegal class B : A { // ERROR! Can't derive from class A // }

As the comments imply, it is illegal for B to inherit A because A is declared as sealed One other point: sealed can also be used on virtual methods to prevent further overrrides For example, assume a base class called B and a derived class called D A method declared virtual in B can be declared sealed by D This would prevent any class that inherits D from overriding the method This situation is illustrated by the following:

A glance at Figure 827 shows that the horizontal planar slice of the tank, at the level x feet below the top, is a disc of radius 100 x 2 This disc therefore has area A( x) = ( 100 x 2 ) Thus a slice at that level of thickness

class B { public virtual void MyMethod() { /* */ } } class D : B { // This seals MyMethod() and prevents further overrides sealed public override void MyMethod() { /* */ } } class X : D { // Error! MyMethod() is sealed! public override void MyMethod() { /* */ } }

C# defines one special class called object that is an implicit base class of all other classes and for all other types (including the value types) In other words, all other types are derived from object This means that a reference variable of type object can refer to an object of any

Part I:

and (assuming that water weights 624 pounds per cubic foot) weight equal to w( x) = 624 ( 100 x 2 ) x