The density of a certain type of wood is 353 kilograms per cubic meter. A sample of this type of wood is in the shape of a cube and has a mass of 345 kilograms. To the nearest hundredth of a meter, what is the length of one edge of this sample?

Question

Accepted Answer

Choice B is correct. It’s given that the density of a certain type of wood is 353 kilograms per cubic meter ( kg/m 3 ), and a sample of this type of wood has a mass of 345 kg. Let x represent the volume, in m 3 , of the sample. It follows that the relationship between the density, mass, and volume of this sample can be written as 353 kg ⁄ 1 m 3 = 345 kg ⁄ x m 3 , or 353 = 345 ⁄ x . Multiplying both sides of this equation by x yields 353x = 345. Dividing both sides of this equation by 353 yields x = 345 ⁄ 353 . Therefore, the volume of this sample is 345 ⁄ 353 m 3 . Since it’s given that the sample of this type of wood is a cube, it follows that the length of one edge of this sample can be found using the volume formula for a cube, V = s 3 , where V represents the volume, in m 3 , and s represents the length, in m, of one edge of the cube. Substituting 345 ⁄ 353 for V in this formula yields 345 ⁄ 353 = s 3 . Taking the cube root of both sides of this equation yields 3 √ 345 ⁄ 353 = s, or s ≈ 0.99. Therefore, the length of one edge of this sample to the nearest hundredth of a meter is 0.99. Distractor Explanations: Choices A, C, and D are incorrect and may result from conceptual or calculation errors.

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