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?
- A. 2
- B. 3
- C. 4 ✓
- D. 6
Correct Answer: C. 4
Explanation
The dimensions of the open box formed will be (24-2x), (18-2x), and x. Its volume is x(24-2x)(18-2x) = 640. Checking the given options: if x=4, the volume is 4(24-8)(18-8) = 4 \times 16 \times 10 = 640, which satisfies the equation.
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