A piece of tin is in the form of a rectangle having length 12 cm and width 8 cm. This is used to construct a closed cube. The side of the cube is :
- (a) 2 cm
- (b) 3 cm
- (c) 4 cm ✓ UPSC's answer
- (d) 6 cm
Why the answer is (c)
• The area of the rectangular tin is calculated as length multiplied by width: 12 cm × 8 cm = 96 cm².
• Since the tin is used to construct a closed cube, the total surface area of the cube must equal the area of the tin.
• The formula for the total surface area of a cube is 6s², where s is the side length.
• Equating the areas gives 6s² = 96 cm².
• Solving for s² yields s² = 16 cm², and taking the square root gives s = 4 cm.
• Therefore, the side of the cube is 4 cm, which corresponds to option (c).
Why the other options are wrong
- (a) 2 cm
- A side of 2 cm would result in a total surface area of 24 cm², which is not equal to the tin's area of 96 cm².
- (b) 3 cm
- A side of 3 cm would result in a total surface area of 54 cm², which is not equal to the tin's area of 96 cm².
- (d) 6 cm
- A side of 6 cm would result in a total surface area of 216 cm², which exceeds the tin's area of 96 cm².
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.