Question

If the density of the fuel is 0.821 g/ml, what mass of fuel has the airplane taken on?

Answer 1

The mass of the fuel carried on the aircraft is $\boxed{167.89\,{\text{kg}}}$.

Further Explanation:

Given:

The density of the fuel carried by the aircraft is $0.821\,{{\text{g}} \mathord{\left/{\vphantom {{\text{g}} {{\text{ml}}}}} \right.\kern-\nulldelimiterspace} {{\text{ml}}}}$.

The volume of the fuel carried by the aircraft is $245\,{\text{litres}}$.

Concept:

The density of an object is defined as the amount of mass contained per unit volume of the object. It is given as the ratio of the mass and volume of the object. The units of density are ${{\text{g}} \mathord{\left/{\vphantom {{\text{g}} {{\text{ml}}}}} \right.\kern-\nulldelimiterspace} {{\text{ml}}}},\,{{{\text{kg}}} \mathord{\left/{\vphantom {{{\text{kg}}} {{{\text{m}}^{\text{3}}}}}} \right.\kern-\nulldelimiterspace} {{{\text{m}}^{\text{3}}}}},\,{{\text{g}} \mathord{\left/{\vphantom {{\text{g}} {{\text{c}}{{\text{m}}^{\text{3}}}}}} \right.\kern-\nulldelimiterspace} {{\text{c}}{{\text{m}}^{\text{3}}}}}$ etc.

The density of an object can be expressed mathematically as.

  $\boxed{\rho = \frac{m}{V}}$

Rearrange the above expression for the mass of the fuel in the aircraft.

  $\boxed{m = \rho \cdot V}$

Convert the density of the fuel into ${{{\text{kg}}} \mathord{\left/{\vphantom {{{\text{kg}}} {{\text{litre}}}}} \right.\kern-\nulldelimiterspace} {{\text{litre}}}}$.

$\begin{aligned}\rho&= 0.821\,{{\text{g}} \mathord{\left/{\vphantom {{\text{g}} {{\text{ml}}}}} \right. \kern-\nulldelimiterspace} {{\text{ml}}}}\left( {\frac{{1\,{\text{kg}}}}{{1000\,{\text{g}}}}} \right)\left( {\frac{{1000\,{\text{ml}}}}{{1\,{\text{litre}}}}} \right)\\&= 0.821\,{{{\text{kg}}} \mathord{\left/ {\vphantom {{{\text{kg}}} {{\text{litre}}}}} \right.\kern-\nulldelimiterspace} {{\text{litre}}}}\\\end{aligned}$  

Substitute the values of density and volume in above expression.

$\begin{aligned}m&= 0.821\,{{{\text{kg}}} \mathord{\left/{\vphantom {{{\text{kg}}} {{\text{litre}}}}} \right.\kern-\nulldelimiterspace} {{\text{litre}}}} \times 245\,{\text{litre}}\\&= {\text{201}}{\text{.145}}\,{\text{kg}}\\\end{aligned}$  

Thus, the mass of the fuel carried by the aircraft is $\boxed{201.145\,{\text{kg}}}$.

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Answer Details:

Grade: High School

Chapter: Density and Volume

Subject: Physics

Keywords:  Density, aircraft, fuel, ratio of mass and volume, amount of mass contained, 0.821g/ml, 245 l, physical properties, per unit volume.

Answer 2

Mass of fuel has the airplane took on = 167.89 kg

$\boxed{\boxed{\bold{Further~explanation}}}$

Density is a quantity derived from the mass and volume

density is the ratio of mass per unit volume

With the same mass, the volume of objects that have a high density will be smaller than objects with a smaller type of mass

The unit of density can be expressed in g / cm3 or kg / m3

• Density formula:

$\large{\boxed{\bold{\rho~=~\frac{m}{V} }}}$

ρ = density

m = mass

v = volume

A common example is the water density of 1 gr / cm3

If we look at fuel capacity data such as Airbus which has a maximum capacity of 204, 5 liters then the mass of fuel it carries is

ρ = 0.821 gr / ml = 0.821 kg / l

• mass = ρ . V

mass = 0.821 kg / l . 204.5 liters

mass = 167.89 kg

So the mass of fuel carried by aircraft is 167.89 kg

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Keywords: density, mass, volume, aircraft, fuel, derivative quantities