Asteroid is in the shape of sphere and has a mass of 1000 kilograms. Determine t

Question

Asteroid is in the shape of sphere and has a mass of 1000 kilograms. Determine the density (in grams per cubic centimeter) of this asteroid if its diameter is known to be 1.2 meters. Useful information: 1 kg = 1000 g, 1 m = 100 cm, volume of sphere = 4/3 pi r^3. Remember that the radius of a sphere is equal to half its diameter! How does your calculated density (in grams per cubic centimeter) compare to the density of water? Would you expect this asteroid to float or sink in water based on your calculations?  Show all of your work.

Explanation / Answer

To determine the density you can use the basic density equation of d=m/v You are given the mass (1000 kg) and the volume can be calculated using v=4/3pi*r^3 which would give you a volume of .905 meters cubed Substitute these values into the density equation as follows - d= 1000kg/.905cubic meters which will give you 1104.97kg/cubic meter In this problem you are looking for an answer in grams/cubic centimeter so you would have to apply a factor of ten (because there are 1000g in 1kg and 100cm in 1m) which would make you answer equal to 11049.7g/cubic cm The second part asks for a comparison to the density of water (density of water is 1g/cubic cm) so you could compare using a simple ratio i.e. 11049/7:1 If the density of the asteroid is greater than the density of water, then of course it would sink (basic properties of buoyancy)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.