+1 vote
101 views Options are

A) 1:3^(1/3)  B) 3^(1/3):1 C) 3:1 D) 3^(2/3):1

| 101 views

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 =  πR(as r = h)

Let radius of cone = Rc and height be h' and Rc=h' given

Volume of cone =  πr2h/3 = π(Rc)

Given:

Volume of cylinder =  πr2h =  πR= 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

R = cyclinder radius or height

so answer is D Rc:R = (3)2/3:1

by Active (2.3k points)
selected