Question

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

Answer 1

The ratio between radius and height = 5 : 12 

Volume = 2512 cubic cm 

Let radius (r) = 5x, height (h) = 12x and slant height = l 

  

l² = r² + h² 

`=>` l² = (5x)² + (12x)² 

`=>` l² = 25x² + 144x²  

`=>` l² = 169x² 

`=>` l = 13x  

Now volume = `1/3pir^2h` 

`=> 1/3pir^2h = 2512` 

`=> 1/3(3.14)(5x)^2(12x) = 2512` 

`=> 1/3(3.14)(300x^3) = 2512` 

∴ `x^3 = (2512 xx 3)/(3.14 xx 300)`

= `(2512 xx 3 xx 100)/(314 xx 300)`

= 8 

`=>` x = 2 

∴ Radius = 5x = 5 × 2 = 10 

Height = 12x = 12 × 2 = 24 cm 

Slant height = 13x = 13 × 2 = 26 cm