Question

What is the density of an object with a mass of 24 grams and volume of 30 cubic centimeters?

Answer 1

Answer: The density is: "0.8 g per cubic centimeter" ;

or: write as "0.8 g per cm³ ."

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Step-by-step explanation:

Note that:

"
`D=m/V` " ;

that is: Density = mass
`per` unit volume;

The equation is "mass divided by Volume".

Since even in equation form; the equation is "mass per [unit] volume" ;

We can solve this problem as a "unit rate problem"—albeit within

the conventional standard "units" used as appropriately and customarily.

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So: Using this equation—Solve for: " ____" :

→
`D=m/V`

in which:

D refers to: Density ; for which we shall solve.

m refers to: mass ;

[Note: By convention; in units of "grams" [or; "g"] } ;

"V" refers to "Volume";
[Note: By convention; in single "stand-alone units."].
of: "mL" [milliliters] ; or: "cubic centimeters" [cm³ ] ;
→ Note that usually, "mL" is the most commonly used "unit" for measuring liquids/solvents—and that "cm³ "; that is: "cubic centimeters"
—is the most commonly used "unit" for measuring the volume of solids—such as within this very question.}.

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So, we are given: " m = 24 g "; and: " V = 30 cubic centimeters" ;

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Plug this into the equation for "Density; "D" ; and solve:

`D = (m)/(V) = (24g)/(30CubicCentimeters) =(24)/(30)`
`D = (m)/(V) = (24g)/(30CubicCentimeters) =((24)/(30)) (g)/(CubicCentimeter)`;
↔
`(24)/(30)=((24/6))/((30/6))=(4)/(5)` ;
Let us convert our fraction to a decimal form; since a density value of a fraction is awkward.
→
`(4)/(5) = (?)/(10)` ;

To find the "?" value, here is the explanation: We use the value of "10" as the denominator to help convert this value to "decimal form".

Cross-factor multiply.
That is: Given:

`(a)/(b) = (c)/(d)` ;
`b\\eq 0` ;
`d`
`\\eq 0` ;

⇒ "
`ad = bc` " ;

Thus: 10(4) = 5(?) ;
→ 40 = 5*(?) ; Now: divide each side by "5" ; to solve for: "?"

40/5 = 5(?) / 5 ;

→ "?" = 8 ;

So: "4/5" = "8/10" ; that is: "(8÷10)" = 8. ÷ 10 = 0.8

The density; D of the object [described in the question]:

is: "0.8 g per cubic centimeter" ;

or: write as: "0.8 g per cm³ " .
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Hope this is helpful to you. Best wishes!