anonymous
  • anonymous
The mass of a sphere M varies directly as the cube of the radius r. If M = 0.54 kilograms when r = 3 centimeters, what is the mass of the sphere, made of the same material, with a radius of 5 centimeters?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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whpalmer4
  • whpalmer4
\[M = kr^3\]If you increase the radius by a factor of 5/3, the mass changes by a factor of (5/3)^3.
anonymous
  • anonymous
2.5 kilograms is what i got but not entirely sure
whpalmer4
  • whpalmer4
You should be sure :-)

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anonymous
  • anonymous
Thanks
whpalmer4
  • whpalmer4
This may not be the way they expected you to solve this (probably wanted you to solve \(M = kr^3\) for \(k\) when you know \(M\) and \(r\) and use that to find the new M\) but for these scaling problems, just replace the dimensions with the scaling factors to get the overall change. Surface area of a sphere when the radius doubles? Well, surface area of sphere is proportional to r^2, so (2)^2 = 4, surface area doubles. Etc.
whpalmer4
  • whpalmer4
Surface area quadruples, that is, not doubles...
whpalmer4
  • whpalmer4
Or more usefully, radius of pizza doubles, therefore area of pizza goes up by (2)^2 = 4 :-)
anonymous
  • anonymous
Thanks alot for that information

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