SAT Math Multiple Choice Question 981: Answer and Explanation

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Question: 981

1.

A flooring company stores its marble tiles in vertical stacks as shown above. Eachtile measures. How many cubic feet of tile are there in one stack of 48 of these tiles?

  • A. 4.5
  • B. 54
  • C. 162
  • D. 648

Correct Answer: A

Explanation:

A

Difficulty: Easy

Category: Additional Topics in Math / Geometry

Strategic Advice: There are a number of ways to approach a question like this, but each approach must include converting the dimensions of the tiles from inches to feet.

Getting to the Answer: It is easier to convert inches to feet than cubic inches to cubic feet, so start by converting each of the dimensions of the tile to feet. There are 12 inches in 1 foot, so the dimensions of a single piece of tile are (18 ÷ 12) × (18 ÷ 12) × (0.5 ÷ 12) or, when simplified,. The stack of tiles takes on the shape of a right rectangular prism, so you can find the volume using the formula V = lwh. You already know the length (1.5 ft) and the width (1.5 ft). To find the height, multiply the height of one tile by the number of tiles in the stack: feet. This means the number of cubic feet in the stack of tiles is 1.5 × 1.5 × 2 = 4.5, making (A) correct.

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