We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm $$\times$$ 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is _______.

Items	Cost	Profit%	Marked price
P	5400	-	5860
Q	-	25	10000

Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3 : 4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost

(Profit% = $${{Selling\,price - Cost} \over {Cost}} \times 100$$).

The discount on item Q, as a percentage of its marked price, is ________.

Two straight lines are drawn perpendicular to each other in X-Y plane. If $$\alpha $$ and $$\beta $$ are the acute angles the straight lines make with the X-axis, then $$\alpha $$ + $$\beta $$ is ______.

The figure below shows an annular ring with outer and inner radii as b and a, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is _______.