Answer:
The total surface area of these N spherical droplets is 4.4929 m²
Explanation:
From the information given :
assuming that :
30 cm³ of gasoline is atomized into N spherical droplets &
each with a radius of 2.0 × 10−5 m
We are tasked to determine the total surface area of these N spherical droplets
We all known that:
[tex]1 \ cm^3 = 10 ^{-6} m^3[/tex]
Therefore
[tex]30 \ cm^3 = 30 * 10 ^{-6} m^3 = 3 *1 0^{-5} \ m^3[/tex]
For each droplet; there is a required volume which is = [tex]\dfrac{4}{3} \pi r ^3[/tex] since it assumes a sphere shape .
Thus;
replacing radius(r) with 2.0 × 10−5 m; we have:
[tex]= \dfrac{4}{3} \pi * (2.0 *10^{-5} m) ^3[/tex]
= [tex]3.35 * 10^{-14} \ m^3[/tex]
However; there are [tex]3*10^{-5} \ m^3[/tex] gasoline atomized into N spherical droplets with each with radius 2.0 × 10−5 m
For N ; we have ;
[tex]=\dfrac{3*10^{-5} \ m^3}{3.35 * 10^{-14} \ m^3/ droplet}[/tex]
= [tex]8.95*10^8 \ droplet s[/tex]
So; each droplet have a surface area = [tex]4 \pi r^2[/tex]
= [tex]4 \pi (2.0*10^{-5}m) ^2[/tex]
= [tex]5.02*10^{-9} \ m^2/droplets[/tex]
The surface area per droplet is equivalent to [tex]5.02*10^{-9} \ m^2/droplets[/tex]
Thus;
The total surface area of these N spherical droplets will be :
= [tex]8.95*10^8 \ droplet s * 5.02*10^{-9} \ m^2/ droplets[/tex]
= 4.4929 m²
The total surface area of these N spherical droplets is 4.4929 m²
