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The dimension in centimeter of rectangular box R is 6 by 8 by 10. Which of the following cannot be total surface area, in square centimeters of two faces of R? A. 96 B. 120 C. 118 D. 160

1 Answer

Jun 26, 2018

$C. 118$ $"C. 118"$

Explanation:

Given

$l = 6$ $"l = 6"$
$b = 8$ $"b = 8"$
$h = 10$ $"h = 10"$

Sum of surface areas of two opposite faces

$lb + lb = (6 \times 8) + (6 \times 8) = 96$ $"lb + lb = (6 × 8) + (6 × 8) = 96"$
$bh + bh = (8 \times 10) + (8 \times 10) = 160$ $"bh + bh = (8 × 10) + (8 × 10) = 160"$
$lh + lh = (6 \times 10) + (6 \times 10) = 120$ $"lh + lh = (6 × 10) + (6 × 10) = 120"$

Sum of surface areas of two adjacent faces

$lb + lh = (6 \times 8) + (6 \times 10) = 108$ $"lb + lh = (6 × 8) + (6 × 10) = 108"$
$lb + bh = (6 \times 8) + (8 \times 10) = 128$ $"lb + bh = (6 × 8) + (8 × 10) = 128"$
$bh + lh = (8 \times 10) + (6 \times 10) = 140$ $"bh + lh = (8 × 10) + (6 × 10) = 140"$

$118$ $"118"$ is missing in both the cases.

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