2022 · Q82
A rectangular metal sheet is of length 24 cm and breadth 18 cm. From each of its corners a square of side x cm is cut off and an open box is made of the remaining sheet. If the volume of the box is 640 cubic cm, then what is the value of x?
Elementary MathematicsMensuration
- A2
- B3
- C4
- D6
Explanation
(24−2x)(18−2x)x = 640: x = 4 gives 16×10×4 = 640 (x = 2 gives 560, x = 3 gives 648). Since x must be less than half the breadth (9 cm), only the smaller root of the cubic is admissible — here direct trial is fastest. The keyed option is C.