Hi
Volume of sphere = 4/3πr^{3}
Dividind it into 2 parts : 1:3 ratio so partition ratios = 1/4 : 3/4
Now 1/4 of 4/3πr^{3 = }1/3πr^{3}
and 3/4 of 4/3πr^{3 = }πr^{3}
Let radius of cylinder = R and height be h' and R=h' given
Volume of cylinder = πr^{2}h = πR^{3 }(as r = h)
Let radius of cone = Rc and height be h' and Rc=h' given
Volume of cone = πr^{2}h/3 = π(Rc)^{3 }
Given:
^{ }Volume of cylinder = πr^{2}h = πR^{3 }= smaller part = 1/3πr^{3}
Divding πR^{3 }and 1/3πr^{3} we get (R/r) =(1/3)^{1/3 } equation 1
Volume of cone = πr^{2}h/3 = π(Rc)^{3}/3^{ }^{ }= larger part = ^{ }πr^{3}
Dividing above we get (Rc/r) = (3)^{1/3 } equation 2
Dividing equation 1 and 2
(Rc/r) / (R/r) = (3)^{1/3 }/^{ }(1/3)^{1/3 }
Rc/R = (9)^{1/3}
as we know 9 = 3^{2}
Rc/R = (3)^{2/3}
Here Rc= cone radius
R = cyclinder radius or height
so answer is D Rc:R = (3)^{2/3}:1