Hi
Volume of sphere = 4/3πr3
Dividind it into 2 parts : 1:3 ratio so partition ratios = 1/4 : 3/4
Now 1/4 of 4/3πr3 = 1/3πr3
and 3/4 of 4/3πr3 = πr3
Let radius of cylinder = R and height be h' and R=h' given
Volume of cylinder = πr2h = πR3 (as r = h)
Let radius of cone = Rc and height be h' and Rc=h' given
Volume of cone = πr2h/3 = π(Rc)3
Given:
Volume of cylinder = πr2h = πR3 = smaller part = 1/3πr3
Divding πR3 and 1/3πr3 we get (R/r) =(1/3)1/3 equation 1
Volume of cone = πr2h/3 = π(Rc)3/3 = larger part = πr3
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 = 32
Rc/R = (3)2/3
Here Rc= cone radius
R = cyclinder radius or height
so answer is D Rc:R = (3)2/3:1