The volume of Neptune is on the order of 10^23 m^3 (a) What is this in cubic kilometers (km^3)? (b) What is it in cubic miles (mi^3)? (c) What is it in cubic centimeters (cm^3)?

Answer 1

Hi.

a. Let's start by converting cubic meters to cubic kilometers. To do that, I look up the conversion factor, which is that there are 1.0 x 10⁹ cubic meters in each cubic kilometer.

1.0 x 10²³ m³ x 1.0 km³ / 1.0 x 10⁹ m³ = 1.0 x 10¹⁴ km³

b. Now we have to convert from cubic meters to cubic miles. Again, I look up the conversion factor, which is that one cubic mile is equal to 4.168 x 10⁹ cubic meters.

1.0 x 10²³ m³ x 1.0 cubic mile / 4.168 x 10⁹ m³ = 2.4 x 10³³ cubic miles

c. This time we will go from cubic meters to cubic centimeters. Since the unit to which we will convert is smaller than the one from which we convert, we expect the magnitude to increase. The conversion factor is 1,000,000 cubic centimeters per cubic meter.

1.0 x 10²³ m³ x 1.0 x 10⁶ cm³ / 1.0 m³ = 1.0 x 10²⁹ cm³