Question

The radius and the height of right circular come are in the ratio 5:12 and it's volume is 314 cubic metre , then find the slant height of the cone

Answer 1

For this we need to find radius and height.
Let radius be 5x and height be 12x respectively
So, we know, 
Volume of cone ⇒ 1/3πr²h
                          ⇒ 1/3π(5x)²(12x) = 314
                          ⇒ 3.14(25x²)(12x) = 314 × 3
                          ⇒ x³ = 314 × 3/3.14×25×12
                          ⇒ x³ = 1
                          ⇒ x = 1
So, Radius = 5 × 1 = 5 cm
      Height = 12 × 1 = 12 cm
We know,
Slant height = √(r)² + (h)²
                    = √(5)² + (12)²
                    = √25 + 144
                    = √169
                    = 13 cm      
∴ Slant height of cone = 13 cm