Develop a class hierarchy of shapes and write a program that computes the amount of paint needed to paint different objects. The hierarchy will consist of a parent class Shape with three derived classes $-$ Sphere, Rectangle, and Cylinder. For the purposes of this exercise, the only attribute a Shape will have is a name, and the method of interest will be one that computes the area of the shape $($surface area in the case of three$-$dimensional shapes$).$ You have been provided with an abstract class Shape.

You must produce output in the precise form shown in the "Example Interaction" below, and you must write and use $($at least$)$ the following public classes or methods as part of your solution:

$($a$)$ Define a class Sphere which inherits from Shape and implements its abstract methods. A sphere has an instance variable radius which is initialised in the parameterised constructor for the class. A sphere's area $($surface area$)$ is given by the formula $4****$ radius ${?}^2.$

$($b$)$ Define similar classes for a rectangle and a cylinder. Both the class Rectangle and Cylinder are descendants of the class Shape. A rectangle is defined by its instance variables length and width which are initialised in its parameterised constructor, and its area is the length $**$ width. Similarly a cylinder is defined by a its instance variables radius and height which are initialized by its parameterised constructor, and its area $($surface area$)$ is $**$ radius ${?}^2**$ height. Define the toString $()$ method for each class in a way similar to that for the Sphere class.

$($c$)$ Define a class Paint which has an instance variable coverage which is initialized $($e$.$g$.350)$ by its parameterised constructor, and a method double amount $($Shape$)$ which takes in an object $($Sphere$,$ Rectangle, or Cylinder$)$ as a parameter. The method computes and returns the amount of paint needed to paint a shape. Use the fact that the amount of paint needed is the area of the shape divided by the coverage for the paint. Hint $-$ amount $()$ should invoke the toString $()$ method of the object.

$($d$)$ In your main $()$ method instantiate three objects of type Shape: deck to be a $20$x$35$ foot Rectangle, bigBall to be a Sphere of radius $=15,$ and tank to be a Cylinder of radius $=10$ and height $=30,$ and compute the amount of paint needed to paint each shape. Make the appropriate method calls to assign the correct values to the three amount $()$ parameters by making use of Java's Polymorphic properties.

Example Interaction:

Computing amount for Rectangle of length $20\mathrm{.}0$ and width $35\mathrm{.}0$

Amount of paint required is $2\mathrm{.}0$

Computing amount for Sphere of radius $15\mathrm{.}0$

Amount of paint required is $8\mathrm{.}078381109230897$

Computing amount for Cylinder of radius $10\mathrm{.}0$ and height $30\mathrm{.}0$

Amount of paint required is $26\mathrm{.}927937030769655$