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A small airplane takes on 245 L of fuel. If the density of the fuel is 0.821 g/ml, what mass of fuel has the airplane taken on?

In this question, we have to find the mass of the fuel with which the airplane took off from the runway while the amount of fuel in liters and the density are known. The basic concept behind this question is the knowledge of density and mass. We should know the difference between these two physical quantities, the formula for calculating mass and density, and the relationship between them as well.

In physics, density is represented as mass per unit volume. Density is represented by the symbol $\rho $, whereas in mathematics we can write it as mass being divided by the volume.

\[ Density = \dfrac{Mass}{Volume} \]

Which can also be written as:

\[ \displaystyle \rho = \dfrac{m}{V} \]

Here in this formula, we have:

$m\ =\ Mass \space of \space the \space object $

$V\ =\ Volume \space of \space the \space object $

$\rho\ =\ Density$

The unit of density will be the unit of mass over the unit of volume, which is defined as grams per centimeters cube $\dfrac {g}{cm^3 }$ or kilograms per liter $\dfrac {Kg}{L }$

In physics, the term mass implies how much matter is enclosed within an object.

Mass determines how much inertia is within the object, whereas density determines the degree of compactness (how close the atoms are together within the substance).

\[ Mass = Density \space \times \space Volume \]

Which can also be written as:

\[ m = \rho \space \times \space V \]

Here in this formula, we have:

$m\ =\ Mass \space of \space the \space object $

$V\ =\ Volume \space of \space the \space object $

$\rho\ =\ Density$

The unit of mass is kilograms $Kg $ or grams $g $

Expert Answer

Given in the question statement:

$Volume\ =\ V =\ 254 L =254 \times 10^3 mL$

$Density = \rho = 0.821$ $\dfrac { g}{ mL }$

Now to calculate the mass, we will use the formula:

\[m = \rho \space \times \space V \]

Now putting values in the above equation, we get:

\[m = 0.821 \times \space 245 \times 10^3\]

\[m=201145\ g\]

Numerical Results

A small airplane took off with the mass of fuel to be $m= 201145g$ when the volume of the fuel was $254 L$ and the density of the fuel was $0.821$ $\dfrac { g}{ mL }$.

\[m = 201145\ g \]

Example

A small plane takes on the fuel of $245 L$. If the mass is $201145 g$, calculate the density of the fuel in grams per milliliter with which the airplane has taken off.

Given in the question statement:

$Volume\ =\ V =\ 254 L=254 \times 10^3 mL$

$mass =\ m = 201145 g$

Now to calculate the density, we will use the formula:

\[\displaystyle \rho = \dfrac{m}{V} \]

Now putting values in the above equation, we get:

\[\rho =\dfrac{201145}{ 245 \times 10^3}\]

\[ Density = \rho = 0.821 \dfrac { g}{ mL }\]

Thus, the required density is:

\[\rho = 0.821 \dfrac { g}{ mL }\]

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