Answer
Plot $III$
Work Step by Step
Given : $x=cos^{3}u cos^{3}v$
$y=sin^{3}u cos^{3}v$
$z=sin^{3}v$
To find the grid curves corresponding to $u$ as constant , substitute $v=k$
$x=cos^{3}u cos^{3}k$
$y=sin^{3}u cos^{3}k$
$z=sin^{3}k$
This represents a family of astroid parallel to $xy$ plane with parameter $a=cos^{3}k$
Only Plot $III$ contains astroid as grid curves.
