A solid right-circular cylinder whose radius of the base is 22.5 cm and whose height is 24 cm is melted and moulded in the shape of a right-circular cone whose radius of the base is 36 cm. What will be the height of this cone?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 28.125 cm.
Volume of a cylinder = π × radius² × height
Volume of a cone = (1/3) × π × r2 × h
According to the question,
Volume of cylinder = Volume of Cone
⇒ π × (R)2 × H = (1/3) × π × r2 × h
⇒ (R)2 × H = (1/3) × r2 × h
⇒ h = ((22.5)2 × 24 × 3)/(36)2
⇒ h = (506.25 × 24 × 3)/1296
⇒ h = 36450/1296 = 28.125 cm
A solid right-circular cylinder is melted and molded into the solid right-circular cone then
The height of this cone is 28.125 cm