Question

An object weighing 1.840 kg has a volume of 0.0015 m³. What is the density of the object in g/cm³? A) 1.2 B) 0.0012 C) 0.82 D) 0.0028 E) none of the above

Answer 1

1.2 g/cm³

Explanation:

Density is mass divided by volume: D = m/V

We're given m and V, but their units don't match "the density of the object in g/cm³". So let's convert the mass and volume to suitable units.

1.84 kg x 1000 g/kg = 1,840 grams

Pretty straightforward, right?

The volume is harder. How many cubic centimeters are in a cubic meter? A lot, right? You could look it up, but you can also work it out. Is this a true statement?

1 m = 100 cm

Of course, right? 100 centimeters in a meter. "Centi" even means 100.

So what if we cubed both sides of that?

(1 m)³ = (100 cm)³

1 m³ = 1,000,000 cm³

That's our conversion factor, and it's a huge number, right? But it's correct because you had to cube 100, which means:

100 x 100 x 100 = 1,000,000

So now we can convert the given volume into cm³:

0.0015 m ³ x 1,000,000 cm³/m³ = 1500 cm³

And now we have mass in grams and volume in cubic centimeters, so we can finally plug them into the equation for density:

D = m/V = 1840g/1500cm³ = 1.2 g/cm³

I hope all that made sense, but ask if it didn't. Whenever you have a density-type question, think about the equation and what you know, then solve for the thing you don't know. And keep an eye on the units!