5003 Praxis Practice Test Practice Question
If the lengths of all the edges of the rectangular solid in the preceding figurewere doubled, what would be the surface area, in square inches, of the new rectangular solid?
Correct Answer: C
Rationale: When the lengths of all the edges of a rectangular solid are doubled, the surface area increases by a factor of four. This is because surface area is proportional to the square of the dimensions. If the original dimensions are \( l, w, h \), the original surface area is \( 2(lw + lh + wh) \). Doubling the dimensions results in new dimensions \( 2l, 2w, 2h \), leading to a new surface area of \( 2(2l \cdot 2w + 2l \cdot 2h + 2w \cdot 2h) = 4 \times 2(lw + lh + wh) \). Thus, if the original surface area was 76, the new surface area is \( 304 \).
Options A (152) and B (160) underestimate the increase, while D (320) incorrectly applies the doubling effect, resulting in an overestimation.
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