GATE APTITUDE

Question

Options are

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

Answer 1

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  4/3πr^{3 =}  1/3πr³

and 3/4 of  4/3πr^{3 =}  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

 

Answer 2

Answer is D.