Question

A cylinder of base radius r and height h is dipped vertically to half the height in a bucket full of purple paint. Find the area of the surface which gets painted.

Answer 1

half of the cylinder is dipped in paint so therefore half of total surface area is now purple ...
therefore area of cylinder which has turned purple is 1/2 x total surface area of cylinder
=1/2x2πr(r+h)
=πr(r+h)

Answer 2

Cylinder ( Bucket) :-
r is the radius
h is the height 

According to the Question :-
1/2 * TSA cylinder is dipped in the purple paint.
⇒ 1/2 * 2πr(h+r)
⇒ π*r*h+r
⇒ πrh + πr²

∴ Area of purple paint is πrh + πr²

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Yours, Jahnavi.