Answer to Question #159014 in Algebra for Ali

Question #159014

The mass of a sphere, M, is directly proportional to r cubed, where r is the radius of the sphere in cm

When r = 10 cm, M = 200 grams.


Work out the mass of a sphere, made of the same material, with a radius of 15 cm


1
Expert's answer
2021-01-29T05:03:38-0500
M=Cr3,C=constM=Cr^3, C=const


Solve for CC


C=Mr3C=\dfrac{M}{r^3}

Given M=200 g,M=200\ g, when r=10 cmr=10\ cm


C=200g(10cm)3=0.2 g/cm3C=\dfrac{200g}{(10cm)^3}=0.2\ g/cm^3

When r=15 cmr=15\ cm


M=0.2 g/cm3(15cm)3=675gM=0.2\ g/cm^3\cdot(15cm)^3=675g

When r = 15 cm, M = 675 grams.



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