Question

If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone?  

Answer 1

Let radius of cone is r and height is h 

Volume `V1=1/3pir^2h ` 

In another case, 

Radius of cone = half of radius =` r/2` 

Height =h 

∴ `Volume= (V_2)=1/3pi(1/2r)^2h`

=` 1/3pixxr^2/4xxh` 

= `1/12pir^2h` 

∴ `V_1/V_2=(1/12pir^2h)/(1/3pir^2h)=3/12=1/4` 

∴ Ratio will be (1:4).