Advanced MathMediumExpression for the volume of an open box folded from a square sheet
Advanced Math practice question
A square of side 2 centimetres is cut from each corner of a square sheet of cardboard with side length s centimetres, where s > 4, and the flaps are folded up to make an open box. Which expression gives the volume of the box, in cubic centimetres?
- A. 2(s − 4)²Correct
- B. 2(s − 2)²
- C. (s − 4)²
- D. 4(s − 2)²
Answer: A. 2(s − 4)²
Cutting 2 cm from both ends of each side leaves a base of (s − 4) by (s − 4), and the folded flaps make the height 2. Volume = 2(s − 4)².
Why the other answers are wrong
- B. 2(s − 2)²
- 2(s − 2)² removes 2 cm from only one end of each side.
- C. (s − 4)²
- (s − 4)² is the base area, without the height.
- D. 4(s − 2)²
- 4(s − 2)² uses the wrong base and the square of the height.
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