Question

The radius and height of cone are in the ratio 3 : 4. If its volume is 301.44 cm³. What is its radius? What is its slant height? (Take π = 3.14)

Answer 1

Let the radius of cone be 3x cm and the height 4x cm, then

Volume of cone = `1/3`πr²h

⇒ `1/3` π (3x)² (4x) = 301.44

⇒ x³ = 8
⇒ x = 2
Thus, radius of cone is 6 cm and height 8 cm.
Now,
slant height of cone = `sqrt( (6)^2 + (8)^2)` = 10 cm.