The cylinder has a height of 1.2 m, radius is 0.4 m and is open at the top. The inside surface is painted at a cost of $2.30 per m^2. Calculate the cost of painting the inside surface.

Well, I don't know exactly but I will give it a go.

If you imagine the cyclinder unraveled out to form a rectangle (not including the top and bottom circles).

The height is 1.2m , and the length would be the perimeter of the top circle (or bottom for that matter). 

So perimeter = 2(pi)r = 0.8pi

Area = Length x height = 0.8pi x 1.2 = (24/25)pi (m^2)

+ it says its open at the top(so you don't have to paint that section) but you will have to paint the bottom section:

therefore area of circle = (pi)r^2 = (pi)(0.4)^2 = (4/25)pi (m^2)

Therefore total area = (24/25)pi + (4/25)pi  -->  (29/25)pi (m^2)

Its cost $2.3 each m^2 therefore (29/25)pi * 2.3 = $8.38 (3sf)