Question

The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use it 𝜋 = 3.14). 

Answer 1

Let the ratio be x 

Radius ‘r’ = 5x
Height ‘h’ = 12x  

∴ Slant height `l` `=sqrt(r^2+h^2)=sqrt((5x)^2+(12x)^2)=13x` 

Now volume = `2512cm^3` 

⇒ `1/3xxpixx(5x)^2xx12x=2512`

⇒ `1/3xx3.14xx25x^2xx12x=2512` 

⇒ `x^3=(2512xx3)/(314xx25xx2)` 

⇒ x=2 

∴ Slant height =` 13x=13xx2=26cm` 

And, Radius of cone `=5x=5xx2=10cm`