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?
Answer & explanation
Correct answer: option 1
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