A solid right-circular cylinder, whose radius of the base is 15 cm and height is 12 cm, is melted and moulded into the solid right-circular cone, whose radius of the base is 24 cm. What will be the height of this cone?

14.0625 cm

We know that,

Volume of a cylinder = π × radius² × height 

Volume of a cone = \(\frac{1}{3}\)× π × r² × h

We have,

Radius of the base of a cylinder (R) = 15 cm

Height = 12 cm,

Radius cone (r) = 24 cm.

Volume of cylinder = Volume of Cone

= π × (R)² × H = \(\frac{1}{3}\)× π × r² × h

= (R)² × H = \(\frac{1}{3}\)× r² × h

= h = \(\frac{((15)^2 × 12 × 3)}{ (24)^2}\)

= h = \(\frac{(225 × 36)}{ 576}\)

= h = 14.0625 cm