Aptitude - Volume and Surface Area - Discussion

Take a rectangular sheet of paper. Cut 4 squares at the four corners of the paper. Now fold in the paper at the cut edges to form an open box.

Assume: The length of paper is 48m. Now that two squares of 8m length are removed from corners, length will be reduced to 48 - 8 - 8 = 32. Similarly, breadth will be reduced to 36 - 8 - 8 = 20. The folded-in part of paper, which forms the wall of the open box, is nothing but a side of the square (8m). So volume will be l * b * h.

32 * 20 * 8 = 5120.

Area of remaining box = Area of original box - Area of the 4 squares.
Area of remaining box = (48 * 36) - 4 (8 * 8) = 1728 - 256 = 1472.
But area in the solution is l * b = 32 * 20 = 640.

What is the difference? Please explain me.

Yes, Divya is correct please answer her question,

Area of remaining sheet = (48 * 36) = 1440.
Area of square = 8 * 8 = 64 * 4 = 256.

Balance = 1184.

But 32 x 20 = 512 how?

Nice explanation @Hemant.

16 has been deducted because in one length of 48cm there ill be two corners.

So its really simply to just deduct length of square two times i.e. 2 * 8 = 16 for two square corner at one line.

How did 8 came?

Take a sheet 48*36 cut each corner 8 unit you will get a shape like # this fold it you will get a open box which dimension 32*20*8 unit. Try to imagine or drawing.

Here whether the remaining area after deducting the 4 squares is used for making box if it is so then how 8 will come at the place of height.

How is it clear from question that which area have to be used for box?

How the height of the box is 8?

It is very easy to understand if you try with a paper. When you fold the paper to make a box the height of box will be equal to the square length.