The radius of the planet Saturn is 5.85 ✕ 107 m, and its mass is 5.68 ✕ 1026 kg. (a) Find the density of Saturn (its mass divided by its volume) in grams per cubic centimeter. (The volume of a sphere is given by 4/3 πr3.) g/cm3 (b) Find the surface area of Saturn in square meters. (The surface area of a sphere is given by 4πr2.)

1.) 0.68 g/cm^3

2.) 4.3 × 10^16 m^2

Explanation:

Given that the radius of the planet Saturn is 5.85 ✕ 107 m, and its mass is 5.68 ✕ 1026 kg.

Where (The volume of a sphere is given by 4/3 πr3.)

Substitutes r into the parameters

V = 4/3π × ( 5.85 × 10^7)^3

V = 8.39 × 10^23 m^3

Convert cubic meters to cubic centimeters by multiplying the result by 1000000

V = 8.39 × 10^29 cm^3

The mass in gram will be

5.68 ✕ 10^26 × 1000 = 5.68 × 10^29g

Density = mass/ volume

Substitute all the parameters into the formula

Density = (5.68 × 10^29) / (8.39 × 10^29)

Density = 0.68 g/cm^3

2.) The surface area of a sphere is given by 4πr^2.

Substitute r into the formula

Surface area = 4π × (5.85 ✕ 10^7) ^2

Surface area = 4.3 × 10^16 m^2

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =