2008/09 AHSMC Part 1 Problem 8

Problem 8 of 16

A rectangular box has integral dimensions and volume $2008$ cubic centimetres. In square centimetres, the minimum value of its surface area is

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Solution

Since $2008 = 2 \times 2 \times 2 \times 251$ , the box must be one of $2 \times 4 \times 251$ , $2 \times 2 \times 502$ , $1 \times 8 \times 251$ , $1 \times 4 \times 502$ , $1 \times 2 \times 1004$ and $1 \times 1 \times 2008$ , with respective surface area $3028$ , $4024$ , $4534$ , $5028$ , $6028$ and $8034$ . The answer is (A).

University of Alberta

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