Aptitude - Volume and Surface Area - Discussion

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A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

They have given the length of the square is 8m(one square box is 8, for two square box 8+8)
Draw a rectangular with 48 length and 36 breath after draw 4 square at each corner with 8 m

take the length of rectangular one side=48
the square on both sides of that rectangular length =8+8=16(each square box that we had drawn)
same thing for breath also
36-16=20
(32*20*8)m^2

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.

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.

Given a Rectangular Sheet, same size Squares need to be cut out from the corners of the Rectangular Sheet, so as to make an Open Box. The Length of one side of the Square will be the Height of the Open Box.

Its best visualized by taking a sheet of paper, cut out squares from the corners, and then fold the portion apart from central rectangle in upward manner. This is an open box.

It's is so easy..we have given length 48 and breadth 36 of a box.

Now a square of 8 m is cut from 4 corners of the above box means 4 small boxes at 4 corners of the box are formed. Now we'll find the volume of the remaining box. Now,

New length of the box = 48-(8+8) = 32m,
New breath of the box = 36-(8+8) = 20m,
New height = 8m.
So volume = l*b*h = 32*20*8 = 5120 cubic meter.

The squares are not used for making that box, the remaining part of the sheet is used for the box.

This sheet has been cut only for making the open box.

If you take base of dimension 32 * 20 then the remaining extra part of the sheet which is also the remaining connected part can be folded to make the open box.

So, now the height of the box is 8 so volume is 32 * 20 * 8.

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.

Your explanation is good shankar.

Here we are removing squares from 2 corners, so there will be 2 squares at each side.

Length of square is given as 8m.

=>length of squares= 8m+8m=16m.

So 16m is subtracted from length and breadth of rectangle.

Hope you understand.

The height will be 8m because the square of 8m is given and it is square so length will be nothing but height.

Imagine a square of 8m it has only two parameters.

Length and breadth, when that square is placed in rectangle then length will be height.