Question

A solid cylinder of brass 9m high and 4m in diameter is melted and recast into a cone of diameter 3m. Find the height of the cone

Answer 1

Given data:

For the cylinder, Diameter = 4m

= > Radius(R) = 2m

Height (H) = 8m

For the cone, Diameter = 3m

= > Radius (r) = 1.5 m

Solution:

Since the metal is melted and re-casted, both the volume of cylinder and cone are equal

Volume of a cylinder = πR²H

Volume of a cone = 1/3 πr²h

πR²H = 1/3 πr²h

= > 2 x 2 x 8 = (1/3) x 1.5 x 1.5 x h

= > h = 42.67 m

Height of the cone = 42.67m