Question

A metallic sheet is of a rectangular shape of dimensions $48m\times 36m$. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8m, then find the volume of the box.

Answer 1

- Hint: When the square of length 8cm is cut from each of the corners, height will become 8. Determine by how much will the length and breadth decrease. Hence determine the volume of the cuboid formed using the volume of the cuboid is given by lbh where l is the length of the cuboid, b is the breadth of the cuboid and h is the height of the cuboid.

Complete step-by-step solution -

When we cut the squares on the corners, OP wil become height , NI will become the length and EH the breadth of the cuboid so formed as shown in the diagram below

Now, we have
AB = 48m, AC = 36m
AE = 8m
Now we have EH = AB-AE-HB = 48-8-8 =32m
IN = BD – IB-ND = 36-8-8=20m
Hence we have the length of the cuboid formed is 32m, the breadth of the cuboid formed is 20m, and the height of the cuboid formed is 8m.
We know that the volume of the cuboid of length l, breadth b and height h is given by V = lbh.
Hence the volume of the cuboid so formed = lbh $=32\times 20\times 8=5120$ cubic metres.
Hence the volume of the cuboid is 5120 cubic metres.

Note: [1] Many students make the mistake of subtracting only the length of the side of the square from each side which is incorrect as twice the length of the side of the square will get cut from each side of the square.