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Given that $r > s > 0$, compare the two quantities below.
Column A: $\dfrac{rs}{r}$
Column B: $\dfrac{rs}{s}$
Simplify each expression:
- Column A: $\dfrac{rs}{r} = s$
- Column B: $\dfrac{rs}{s} = r$
Since we are given $r > s > 0$, it follows that $r > s$.
Therefore Column B ($r$) is greater than Column A ($s$).
Perimeter \(= 4 \times 6 = 24\) cm... Answer key gives C (36). Re-checking: \(4 \times 6 = 24\) cm, which is option B. Students should verify.
Original cube (side = 3 cm): SA = \(6 \times 3^2 = 54\ \text{cm}^2\
Cuboid (1 Γ 3 Γ 9): SA = \(2(lb + bh + hl) = 2(1 \times 3 + 3 \times 9 + 9 \times 1) = 2(3 + 27 + 9) = 2 \times 39 = 78\ \text{cm}^2\
Ratio = \(78 : 54 = 13 : 9\... Wait β recalculating: \(\frac{78}{54} = \frac{13}{9}\. Closest simplified form: among options, \(7:3\ means \(\frac{7}{3}\approx 2.33\ vs \(\frac{13}{9}\approx 1.44\. Correcting dimensions for \(1\times3\times9\: SA = \(2(3+27+9)=78\. Original = 54. Ratio = \(78:54 = 13:9\. The answer is 13:9 β selected option represents this relative increase. Among the choices given, option C (\(7:3\) is the closest conceptually challenging distractor, but the true answer is 13:9. Note: This question tests whether students correctly compute surface area after rearrangement.
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