I take a flat metallic circular plate of radius r. Now by hammering it I now convert it into a metallic hemisphere of same radius as circular plate. What is the change in surface area of the metal due to the hammering?
2πr2
A flat horizontal metal plate consists of 2 sides both circular and having same area.
The area of one side of circular plate= πr2
Since there are 2 sides, area = 2πr2
A metallic hemisphere also consists of 2 sides. Each side has same area.
Area of one hemispherical plate = 2πr2
Since there are 2 sides area = 4πr2
Change in surface area between plate and sphere = 4πr2 - 2πr2 = 2πr2