A metallic Cylinder of radius 8cm and height 2cm is melted and converted into a right circular cone of height 6cm. The radius of the base of the cone is
Given: A metallic Cylinder of radius 8cm and height 2cm
Right circular cone of height 6cm
Volume of a cylinder is given by: π × r2 × h
Volume of a cone is given by: × π × r2 × h
Let V1 be the volume of the Cylinder
∴ V1 = π × r2 × h
⇒ V1 = π × (8)2 × (2) = 128π
Let V2 be the volume of the cone
∴ V2 = × π × r2 × h
⇒ V2 = × π × (r)2 × (6) = 2πr2
Here, Solid Cylinder is melted and made into a Solid cone.
∴ V1 = V2
⇒ 128π = 2πr2
⇒ 2πr2 = 128π
⇒ r2 = = 64
⇒ r2 = 64
⇒ r = √64 = 8cm
∴ Radius of the base of the cone is 8cm.