The basic function of a carburetor of an automobile is to atomize the gasoline and mix it with air to promote rapid combustion. As an example, assume that 30 cm3 of gasoline is atomized into N spherical droplets, each with a radius of 2.0 × 10−5 m. What is the total surface area of these N spherical droplets? [A] m2.

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:

Therefore

For each droplet; there is a required volume which is =  since it assumes a sphere shape .

Thus;

replacing radius(r) with 2.0 × 10−5 m; we have:

=

However; there are gasoline atomized into N spherical droplets with each with radius 2.0 × 10−5 m

For N ; we have ;

=

So; each droplet have a surface area =

=

=

The surface area per droplet is equivalent to

Thus;

The total surface area of these N spherical droplets will be :

=

= 4.4929 m²

The total surface area of these N spherical droplets is 4.4929 m²