A cylinderical oil tube, lying horizontally, has an interior length of 10 cm and aninterior radius 3 cm. If the rectangular surface of the oil has an area of 40 cm?, the depth ofoil in the tube is

We are given the area of ABCD rectangle = 40 sq. cm and the length of the rectangle i.e. AD to be 10 cm.
This gives the length of the breadth of rectangle = 40/10 = 4 cm. 
The breadth i.e. CD is a chord on the circular face. 
However, there are 2 cases when the chord could be of length = 4 cm :

Now, the perpendicular distance of either of the chord from the center can be calculated using Pythagoras theorem in the triangle OPC. This gives OP = $$\sqrt{\ 5}$$ cm.

Thus, the depth of the water could either be R - $$\sqrt{\ 5}$$ OR R + $$\sqrt{\ 5}$$ i.e. $$3-\sqrt{\ 5}\ or\ 3+\sqrt{\ 5}$$ cm.