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?

Question

whpalmer4 · Answer

$$M = kr^3$$If you increase the radius by a factor of 5/3, the mass changes by a factor of (5/3)^3.

anonymous · Answer

2.5 kilograms is what i got but not entirely sure

whpalmer4 · Answer

You should be sure :-)

anonymous · Answer

Thanks

whpalmer4 · Answer

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 · Answer

Surface area quadruples, that is, not doubles...

whpalmer4 · Answer

Or more usefully, radius of pizza doubles, therefore area of pizza goes up by (2)^2 = 4 :-)

anonymous · Answer

Thanks alot for that information