SOLUTION: In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun, but occupying less space than our moon. Suppose that one of these bla

Algebra ->  Conversion and Units of Measurement -> SOLUTION: In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun, but occupying less space than our moon. Suppose that one of these bla      Log On


   

Question 1132685: In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun, but occupying less space than our moon. Suppose that one of these black holes has a mass of 1×10^3 suns and a radius equal to one-half the radius of our moon.
What is the density of the black hole in g/cm^3? The radius of our sun is 7.0×10^5km and it has an average density of 1.4×10^3kg/m^3. The diameter of the moon is 2.16×10^3 miles.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of our sun is:
+V%5Bs%5D+=+%284%2F3%29%2Api%2Ar%5E3+
+V%5Bs%5D+=+%284%2F3%29%2Api%2A%28+7%2A10%5E5+%29%5E3+
+V%5Bs%5D+=+%284%2F3%29%2Api%2A343%2A10%5E15+
+V%5Bs%5D+=+457.333%2Api%2A10%5E15+
+V%5Bs%5D+=+1436.755%2A10%5E15+
+V%5Bs%5D+=+1.436755%2A10%5E21+ km3
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1 m3 = +10%5E%28-9%29+ km3
[ kg/m3 ] x [ m3 / km3 ] = kg/km3
The sun's density is:
+1.4%2A10%5E3%2A10%5E9+ kg/km3
+1.4%2A10%5E12+ kg/km3
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The sun's mass is:
+1.4%2A10%5E12%2A1.436755%2A10%5E21+
+2.011457%2A10%5E33+ kg
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+10%5E3+ suns have a mass:
+2.011457%2A10%5E36+ kg
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To finish, find volume of the moon in km3
Using +V%5Bm%5D+=+%284%2F3%29%2Api%2Ar%5E3+
and divide mass in km to get density in
kg/km3, then use the conversion:
[ kg/km3 ] x [ 1000 g / kg ] x [ 1 km3 / 10^9 m3 ] x [ 1 m3 / 10^6 cm3 ]