SAT Question 7d721177: Ratios Rates Proportional Relationships And Units answer and explanation with Desmos solution

Choice B is correct. It’s given that the density of a certain type of wood is $353$ kilograms per cubic meter $\left({\text{kg/m}}^3\right)$, and a sample of this type of wood has a mass of $345$ kg. Let $x$ represent the volume, in ${\text{m}}^3$, of the sample. It follows that the relationship between the density, mass, and volume of this sample can be written

as $\frac{353\text{kg}}{1{\text{m}}^3}=\frac{345\text{kg}}{x{\text{m}}^3}$, or $353=\frac{345}{x}$. Multiplying both sides of this equation by $x$ yields $353x=345$. Dividing both sides of this equation by $353$ yields $x=\frac{345}{353}$. Therefore, the volume of this sample is $\frac{345}{353}{\text{m}}^3$. 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 ${\text{m}}^3$, and $s$ represents the length, in m, of one edge of the cube. Substituting $\frac{345}{353}$ for $V$ in this formula yields $\frac{345}{353}=s^3$. Taking the cube root of both sides of this equation yields $\sqrt[3]{\frac{345}{353}}=s$, or $s\approx 0.99$. 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.