Question

A) Calculate the average density of the following object (assume it is a perfect sphere). SHOW ALL YOUR WORK (formulas used, numbers plugged in with proper UNITS, and clearly indicate your final answer).

Mass=1.3x1022kg, Diameter=2300km

B) (extra credit problem) Working backwards... Calculate the mean radius of the following object (if it was a perfect sphere).

Density=687kg/m3, Mass=5.68x1026kg

Answer 1

Answers:

A) 2040 kg/m³; B) 58 600 km

Step-by-step explanation:

A) Density

`V = ( 4)/(3 )\pi r^(3) = ( 4)/(3 )\pi* (\text{1150 km})^(3) = 6.37 * 10^(9) \text{ km}^(3)`

`\text{Density} = \frac{\text{mass}}{\text{volume}} = \frac{1.3* 10^(22) \text{ kg} }{6.37 * 10^(9) \text{ km}^(3)}* (\frac{\text{1 km}}{\text{1000 m}})^(3) = \text{2040 kg/m}^(3)`

B) Radius

`\text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{5.68* 10^(26) \text{ kg} }{687 \text{ kg/m}^(3) }= 8.268 * 10^(23) \text{ m}^(3)`

`V = ( 4)/(3 )\pi r^(3)`

`r^(3) = (3V )/(4 \pi )\`

`r= \sqrt [3]{ (3V )/(4 \pi ) }`

`r= \sqrt [3]{ \frac{3* 8.268 * 10^(23) \text{ m}^(3)}{4 \pi } }= \sqrt [3]{ 1.974 * 10^(23) \text{ m}^(3)}= 5.82 * 10^(7) \text{ m}=\text{58 200 km}`