Question

The radius and the height of a right circular cone are in the ratio 5 : 12. If its volume is 314 cubic meter, find the slant height and the radius (Use it 𝜋 = 3.14). 

Answer 1

Let the ratio be x 

∴ Radius `r`= 5x 

Height ‘h’ = 12x 

WKT,  

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

Now volume`=314m^3`           [given data] 

⇒`1/3pir^2h=314m^3 ` 

⇒`1/3xx3.14xx25x^2xx12x=314` 

⇒`x^3=(314xx3)/(3.14xx25xx12)` 

⇒`x^3=1⇒x=1` 

∴ Slant height = 13x=13m 

Radius=5x=5m