The density of a certain type of wood is 353 kilograms per cubic meter. A sample of this type of

Question

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?

A.

$0.98$

B.

$0.99$

C.

$1.01$

D.

$1.02$

Accepted Answer

Choice B is correct. It&rsquo;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 &#160; 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 &#160; kg 1 &#160; m 3 = 345 &#160; kg x &#160; m 3 , or 353 = 345 x . Multiplying both sides of this equation by x yields 353 x = 345 . Dividing both sides of this equation by 353 yields x = 345 353 . Therefore, the volume of this sample is 345 353 &#160; m 3 . Since it&rsquo;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 345 353 3 = s , or s &#8776; 0 . 99 . Therefore, the length of one edge of this sample to the nearest hundredth of a meter is 0.99 . Choices A, C, and D are incorrect and may result from conceptual or calculation errors.

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