Question

Two right circular cone x and y are made x having three times the radius of y and y having half the volume of x. Calculate the ratio between the heights of x and y. 

Answer 1

Let radius of cone y = r

Therefore, radius of cone x = 3r

Let volume of cone y = V

Then volume of cone x = 2V

Let h₁ be the height of x and h₂ be the height of y.  

Therefore, Volume of cone =`1/3pir^2h` 

Volume of cone `x = 1/3pi(3r)^2h_1`

= `1/3pi9r^2h_1`

= `3pir^2h_1` 

Volume of cone `y = 1/3pir^2h_2` 

∴ `(2V)/v = (3pir^2h_1)/(1/3pir^2h_2)` 

`=> 2/1 = (3h_1 xx 3)/h_2 = (9h_1)/h_2` 

`=> h_1/h_2 = 2/1 xx 1/9 = 2/9` 

∴ h₁ : h₂ = 2 : 9