I tried to find the curved surface area of a hemisphere without integration. I found a glitch over there as I didn't found any mistake in my approach. Anyone who has found please do answer.
I got a handle of bucket and I formed a hemisphere by rotating it along the circumference of a imaginary semicircle of same radius 'R'(just for an idea for the figure). I found the curved surface area to be $\pi R \cdot \pi R$=$\pi ^2R^2$.
But it is actually $2\pi R^2$.Figure for help...
It can be a mistake in calculating the circumference of individual lines on the hemisphere. Radius changes as we move outward. So, that can be avoided using Integration.