A metallic sheet of rectangular shape is 48 \text{ cm} \times 36 \text{ cm}. From each corner a square of side x cm is cut off and an open box is made of the remaining sheet. If the box holds 5.12 litre of water, then what is the value of x ?
- A. 6 cm
- B. 7.5 cm
- C. 8 cm ✓
- D. 8.5 cm
Correct Answer: C. 8 cm
Explanation
The volume of the box is V = x(48 - 2x)(36 - 2x) = 5120 \text{ cm}^3 (since 5.12 \text{ L} = 5120 \text{ cm}^3). Testing the options, if x = 8: V = 8 \times (48 - 16) \times (36 - 16) = 8 \times 32 \times 20 = 5120 \text{ cm}^3.
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