I need help solving this problem

Question

Average density of earth is 5.5 g/cm^3

and it weighs 6.0x10^27g. What is the earths volume in cubic kilometers and liters??

Answer 1

Using dimensional analysis:

6.0x10²⁷ g x 1 cm³/5.5 g x 1 L/1x10³ cm³ = 1.09x10²⁴ L = 1.1x10²⁴ Liters

1.1x10²⁴ Liters x 1x10^-12 km³/Liter = 1.1x10¹² km³

Answer 2

Hello, Yesenia,

I just answered another of your questions concerning conversions. Please refer to an explanation that should help with all conversion problems: https://drive.google.com/file/d/1DsD1Wa7KirIn-x3jgtQWQX6BeyjeAKen/view?usp=sharing

5.5 g/cm^3 = density of the Earth

6.0 x 10^27 g is Earth's mass

What is Earth's volume in km^3 and Liters?

Use conversion factors:

1 km = 10^3 m

1 cm = 10^-2 m

10^3 cm^3 = 1 Liter

Please look at the referenced document for directions on how to establish these factors.

With Earth'd density and mass figures, we can calculate Earth's volume:

6.0x10^27 g / 5.5 g/cm^3 = 9.09x10^26 cm^3

By dividing the mass by the density, the grams cancel and cm^3 moves to the top.

But we are asked to express volume in cubic km and L.

1 cm = 10^-5 km

Therefore 1 cm^3 = 10^-5 km

Convert

9.09x10^26 cm^3 * (10^-5 km)/1 cm^3) = 9.09 x 10^11 km^3

The cm^3 cancel, leaving just km^3.

To get Liters:

10^3 cm^3 = 1 Liter

9.09x10^26 cm^3 * (1 Liter/10^3 cm^3) = 9.09 x 10^23 Liters

Practice! I hope this helps,

Bob