Respuesta :
Answer:
volume = 0.029 cm³
Explanation:
We are given that:
mass = 22 mg
We know that:
1 mg = 0.001 grams
This means that:
mass = 22 mg = 0.022 grams
We are also given that:
density = 0.754 g/cm³
Density is calculated using the following rule:
[tex] Density=\frac{mass}{volume} [/tex]
Rewrite the equation to solve for volume:
[tex] volume = \frac{mass}{density} [/tex]
Now, substitute with the values we have:
[tex] volume = \frac{0.022}{0.754} = 0.029 cm^3 [/tex]
Hope this helps :)
The volume of gasoline (in cubic centimeters) is [tex]\boxed{0.029\;\text{cm}^3}[/tex].
Further Explanation:
Density is defined as the mass of the substance per unit volume of the substance. It is denoted by [tex]\rho[/tex]. It is generally expressed in the units of grams per cubic centimeter [tex](\text{g/cm}^3)[/tex]. The formula to calculate the density of a substance is as follows:
[tex]\rho=\dfrac{\text{M}}{\text{V}}[/tex]
Here,
[tex]\rho[/tex] is the density of the substance.
M is the mass of the substance.
V is the volume of the substance.
The formula to calculate the density of gasoline is as follows:
[tex]\text{Denstiy of gasoline}=\dfrac{\text{Mass of gasoline}}{\text{Volume of gasoline}}[/tex] …… (1)
Rearrange equation (2) to calculate the volume of gasoline.
[tex]\text{volume of gasoline}=\dfrac{\text{Mass of gasoline}}{\text{Density of gasoline}}[/tex] …… (2)
The mass of gasoline is 22 mg. This is to be converted into g. The conversion factor for this is,
[tex]1\;\text{mg}=10^{-3}\text{g}[/tex]
Therefore the mass of gasoline can be calculated as follows:
[tex]\begin{aligned}{\text{Mass of gasoline}}&= \left( {22{\text{ mg}}} \right)\left( {\frac{{{{10}^{ - 3}}{\text{ g}}}}{{1{\text{ mg}}}}} \right)\\&= 0.022{\text{ g}} \\ \end{aligned}[/tex]
The mass of gasoline is 0.022 g.
The density of gasoline is [tex]0.754\;\text{g/cm}^3[/tex].
Substitute these values in equation (2).
[tex]\begin{aligned}\text{Volume of gasoline}&=\frac{0.022\;\text{g}}{0.754\;\text{cm}^3}\\&=0.029\text{cm}^3\\\end{aligned}[/tex]
Therefore the volume of gasoline is [tex]0.029\;\text{cm}^3[/tex].
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Answer details:
Grade: Middle School
Chapter: Density
Subject: Chemistry
Keywords: density, mass, volume, 22 mg, 0.022 g, 0.029 cm^3, volume of gasoline, mass of gasoline, density of gasoline, [tex]0.754 \;\text{g/cm}^3, g[/tex], conversion factor.
