Question

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?

• A. 2πr²
• B. 3πr²
• C. 4πr²
• D. πr²

Answer 1

The correct option is A

2πr²

A flat horizontal metal plate consists of 2 sides both circular and having same area.

The area of one side of circular plate= $\pi$$r^2$

Since there are 2 sides, area = 2$\pi$$r^2$

A metallic hemisphere also consists of 2 sides. Each side has same area.

Area of one hemispherical plate = 2$\pi$$r^2$

Since there are 2 sides area = 4$\pi$$r^2$

Change in surface area between plate and sphere = 4$\pi$$r^2$ - 2$\pi$$r^2$ = 2$\pi$$r^2$