Answer to Question #159014 in Algebra for Ali

Question

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

Answer 1

$$M=Cr^3, C=const$$

Solve for $C$

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

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

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

When $r=15\ cm$

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

When r = 15 cm, M = 675 grams.