what is dynamic_cast?

 bool Box::operator==(const Shape& s) const {
  return hght == dynamic_cast(s).hght &&
         wdth == dynamic_cast(s).wdth &&
         dpth == dynamic_cast(s).dpth;
}

Answer:

The cast of the reference to a Shape to a reference to a Box is necessary to enable access to the size instance variables of the Box object. We call this a dynamic cast. Without this cast, the compiler would generate an error to the effect that the size variables are not members of the Shape class:

 bool Box::operator==(const Shape& s) const {
    return hght == s.hght && // ERROR hght is not a member of s
           wdth == s.wdth && // ERROR wdth is not a member of s
           dpth == s.dpth;   // ERROR dpth is not a member of s 
}
On the other hand, receiving a reference to a Box object directly would accept the definition

bool Box::operator==(const Box& s) const { // ERROR does not define
// == const Shape&
return hght == s.hght && wdth == s.wdth && dpth == s.dpth;
}