sat suite question viewer

Problem-Solving and Data Analysis / Ratios, rates, proportional relationships, and units Difficulty: Hard

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?

Back question 31 of 86 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

Explanation

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 $m Superscript 3$ , of the sample. It follows that the relationship between the density, mass, and volume of this sample can be written
as $\frac{353 kg}{1 m^{3}} = \frac{345 kg}{x m^{3}}$ , or $353 = \frac{345}{x}$ . Multiplying both sides of this equation by $x$ yields $353 x equals 345$ . Dividing both sides of this equation by $353$ yields $x = \frac{345}{353}$ . Therefore, the volume of this sample is $StartFraction 345 Over 353 EndFraction m cubed$ . 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 $m Superscript 3$ , and $s$ represents the length, in m, of one edge of the cube. Substituting $StartFraction 345 Over 353 EndFraction$ 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 $s almost equals 0 period 99$ . 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.