SAT Area and volume Practice Question 11 (Hard)

Math · Geometry and TrigonometryHard

The length, width, and height of a rectangular prism are in the ratio $2:3:5$ , and the volume of the prism is $810$ cubic inches. What is the total surface area, in square inches, of the prism?

$279$

$450$

$810$

$558$

Show answer and explanation

Answer: D

Let the dimensions be $2k$ , $3k$ , and $5k$ . Then $30k^3 = 810$ , so $k^3 = 27$ and $k = 3$ , giving dimensions $6$ , $9$ , and $15$ . The surface area is $2(6 \cdot 9 + 6 \cdot 15 + 9 \cdot 15) = 2(54 + 90 + 135) = 558$ square inches.

Choice A adds the three different face areas but forgets that each face appears twice on a prism.

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