Mathematics Areas and Volumes

1. There are two identical circular metal plates. A worker claims that if he
melts these metal plates and recast them into a larger circular metal plate,
the radius of the original metal plate is exactly half of the new one. Do you
agree with him? Explain your answers briefly.
[Hint: The thickness of metal plate can be ignored.]

2. Jenny divides a particular circle into some identical sectors. She finds that
no matter how she divides the circle, the value of the area of each sector is
always equal to the value of the arc length of each sector. Do you think it is
possible? Explain your answer briefly. If it is possible, what is the condition
of the circle?