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# How do you find radius of aluminum sphere using density

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• How do you find radius of aluminum sphere using density
• ### How do you find radius of aluminum sphere using density

Makarmuh > 01-15-2020, 01:07 AM

A solid aluminum sphere has a mass of 83 g.Use the density of aluminum to find the radius of the sphere in inchesExpress your answer using two significant figures.I can\'t figure this out Aluminum has a density of 2.702 g/cm^3. 83 g x (1 cm^3 / 2.702 g) = 30.7 cm^3 That\'s the volume of the Al sphere. The formula for the volume of a sphere is V = (4/3)(pi)(r^3) where r is the radius. 30.7 = (4/3)(3.1416)((r^3) 7.33 = r^3 1.94 cm = r 1.94 cm x (1 in / 2.54 cm) = 0.76 inches.Aluminum\'s density is about 2.7 grams per cubic centimeter. So a sphere with a mass of 84grams has a volume of about 31.111 cubic centimeters. You get this by dividing 84 by 2.7. Now that you know the volume, you can calculate the radius of the sphere. for a sphere, volume = 4/3 pi * radius to the third power. So 31.111 = 4/3 * (3.14...) * r^3. Divide both sides by 4/3 then divide both sides by pi and you get something like r^3 is 7.427. Then find the cube root of this to find your radius. I don\'t have a calculator, so someone should check the numbers.Other related question