Question

Which of the following items would have the lowest density?
OA. A 12 cm3 block of aluminum with a mass of 2 grams
OB. A6 cm3 block of ice with a mass of 4 grams
OC. A 12 cm3 block of wood with a mass of 3 grams
OD. A 2 cm3 block of lead with a mass of 11 grams

Answer 1

Taking into account the definition of density, the correct answer is the option A:  A 12 cm³ block of aluminum with a mass of 2 grams would have the lowest density.

Definition of density

Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space.

In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance.

Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:

$density=\frac{mass}{volume}$

From this expression it can be deduced that density is inversely proportional to volume: the smaller the volume occupied by a given mass, the higher the density.

Different densities

• A 12 cm³ block of aluminum with a mass of 2 grams

In first place, you know that:

1. Mass= 2 grams
2. Volume= 12 cm³

Replacing in the definition of density:

$density=\frac{2 grams}{12 cm^{3} }$

Solving:

density= 0.167 $\frac{grams}{cm^{3} }$

• A 6 cm³ block of aluminum with a mass of 4 grams

On the other side, you know that:

1. Mass= 4 grams
2. Volume= 6 cm³

Replacing in the definition of density:

$density=\frac{4 grams}{6 cm^{3} }$

Solving:

density= 0.667 $\frac{grams}{cm^{3} }$

• A 12 cm³ block of aluminum with a mass of 3 grams

Then, you know that:

1. Mass= 3 grams
2. Volume= 12 cm³

Replacing in the definition of density:

$density=\frac{3 grams}{12 cm^{3} }$

Solving:

density= 0.25 $\frac{grams}{cm^{3} }$

• A 2 cm³ block of aluminum with a mass of 11 grams

Finally, you know that:

1. Mass= 11 grams
2. Volume= 2 cm³

Replacing in the definition of density:

$density=\frac{11 grams}{2 cm^{3} }$

Solving:

density= 5.5 $\frac{grams}{cm^{3} }$

In summary, the correct answer is the option A:  A 12 cm³ block of aluminum with a mass of 2 grams would have the lowest density.

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Answer 2

The item with the lowest density is 12 cm³ block of aluminum with a mass of 2 grams.

What is density?

This is the ratio of mass to volume of an object.

The density of each object is calculated as follows;

• 12 cm³ block of aluminum with a mass of 2 grams;

$\rho = \frac{m}{V} = \frac{2 \ g}{12 \ cm^3} = 0.17 \ g/cm^3$

• 6 cm³ block of ice with a mass of 4 grams;

$\rho = \frac{m}{V} = \frac{4 \ g}{6 \ cm^3} = 0.67 \ g/cm^3$

• 12 cm³ block of wood with a mass of 3 grams;

$\rho = \frac{m}{V} = \frac{3 \ g}{12 \ cm^3} = 0.25 \ g/cm^3$

• 2 cm³ block of lead with a mass of 11 grams;

$\rho = \frac{m}{V} = \frac{11 \ g}{2 \ cm^3} = 5.5 \ g/cm^3$

Thus, the item with the lowest density is 12 cm³ block of aluminum with a mass of 2 grams.

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