Aptitude - Volume and Surface Area - Discussion

How did 8 came?

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.

Nice explanation @Hemant.

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?

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.

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 rectangle= (48 * 36) = 1728.
Area of 4 square's = 4 (8 * 8) = 256.

Remaining area = 1728 - 256= 1472.

Now if we want to directly calculate the area of remaining rectangle, we have to remember that after removing 4 squares from the corner we are left with the shape to whom we can divide into 3 rectangles. 1st the middle portion which has length 32 and breath 36. 2nd has length 8 and breath 20 and 3rd same as 2nd. And now calculate the area for each rectangle you get area = 1472.

The side of the sheet is 32 * 48.

And when we remove 4 squares of side 8 from each corner then the dimension of remaining sheet is (36 - 16) * (48 - 16).
= 20 * 32.

Now when we think to make the wall using square on keeping it's four sides then I think it doesn't make a box because the lower sheet has dimension 32 * 20 but wall has dimension 8*8 then it doesn't properly join the four side.

If we do like this then it has to keep in the dimension of 8 * 8 of the lower sheet also and in that condition, the dimension of the box will be 8 * 8 * 8.

And some part of the lower sheet can not part of the box.

There is a gap between walls then the box is not actually a box it is only like four sheets has been kept normally on a big rectangular ground. And someone is saying it as a box.

How can it possible?

For a box, all of the sides is properly connected.

So I think the answer is wrong.

I am sorry for my previous comment.

The answer is correct.
32 * 20 * 8 is the right answer.

I understand the question correctly and now I am 100% sure the question and answer is correct.