CAT 1991 — QA Question 31
A square piece of cardboard of sides ten inches is taken and four equal squares pieces are removed at the corners, such that the side of this square piece is also an integer value. The sides are then turned up to form an open box. Then the maximum volume such a box can have is
Answer & solution
Correct answer: 72 cubic inches.
72 cubic inches.
- B
24.074 cubic inches.
- C
2000/27 cubic inches.
- D
64 cubic inches.
If x = 1, then for the rectangular box : l = 8, b = 8 and h = 1, so volume = 64.
If x = 2, l = 6, b = 6 and h = 2 and volume = 72.
If x = 3, l = 4, b = 4 and h = 3 and volume = 48.
Therefore, we can see that for a value of x between 2 and 3, the volume of box decreases and will go on decreasing further as x increases.
Hence, the maximum volume that the box can have is 72 cubic inches.
Hence, option (a).