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Square size | Equation for Volume ($V$) |
Value of $x$ that maximizes $V$ |
---|---|---|
$10 \times 10$ | $(10-2x)(10-2x)x$ | $\frac53$ |
$20 \times 20$ | $(20-2x)(20-2x)x$ | $\frac{10}3$ |
$30 \times 30$ | $(30-2x)(30-2x)x$ | $5$ |
$40 \times 40$ | $(40-2x)(40-2x)x$ | $\frac{20}{3}$ |
$50 \times 50$ | $(50-2x)(50-2x)x$ | $\frac{25}{3}$ |
$n\times n$ | $(n - 2x)(n - 2x)x$ | $\frac n6$ |
Paper size | Equation for
Volume ($V$)
|
Value of $x$ that maximizes $V$ |
---|---|---|
$10 \times 10$ | $(10-2x)(10-2x)x$ | $\frac53=1.667$ |
$10 \times 20$ | $(10-2x)(20-2x)x$ | $2.113$ |
$10 \times 30$ | $(10-2x)(30-2x)x$ | $2.257$ |
$10 \times 40$ | $(10-2x)(40-2x)x$ | $2.324$ |
$10 \times 50$ | $(10-2x)(50-2x)x$ | $2.362$ |
$10 \times 1000$ | $ (10-2x)(1000-2x)x$ | $2.494$ |
$10 \times 10000$ | $(10-2x)(10000-2x)x$ | $2.499$ |
Paper size | Value that $x$ approaches as $n$ approaches infinity |
---|---|
$10 \times n$ | $2.5$ |
$1=20 \times n$ | $5$ |
$30 \times n$ | $7.5$ |
$40 \times n$ | $10$ |
$m\times n$ | $\frac m 4$ |