The Volume of two sphere are in the ratio 64:27 find the radii if the sum of the radii is 21cm.

Ratio of the volume of sphere=64:27

that is nothing but 64/27

Volume of the sphere=4/3r³

Sum of the radii=21cm

Let the radius of the first sphere=r₁

Let the radius of the second sphere=r₂

Ratio of the volume of sphere={4/3r₁³ } / {4/3r₂³}

= r₁³ / r₂³

=64/27

=cube roote of 64/27

=4/3

Ratio of the two radii=4:3

Let the ratios be =4xand3x

=4x+3x=21{given}

=7x=21

x=21/7

=3cm

therefore,r₁=4x

=4*3=12cm

and= r₂= 3x =3*3=9cm

therefore, the radii are 12cm and 9cm