Q. 625.0( 1 Vote )

A. 4 cm

B. 5 cm

C. 6 cm

D. 8 cm

Answer :

Given: A metallic Cylinder of radius 8cm and height 2cm

Right circular cone of height 6cm

Volume of a cylinder is given by: π × r^{2} × h

Volume of a cone is given by: × π × r^{2} × h

Let V_{1} be the volume of the Cylinder

∴ V_{1} = π × r^{2} × h

⇒ V_{1} = π × (8)^{2} × (2) = 128π

Let V_{2} be the volume of the cone

∴ V_{2} = × π × r^{2} × h

⇒ V_{2} = × π × (r)^{2} × (6) = 2πr^{2}

Here, Solid Cylinder is melted and made into a Solid cone.

∴ V_{1} = V_{2}

⇒ 128π = 2πr^{2}

⇒ 2πr^{2} = 128π

⇒ r^{2} = = 64

⇒ r^{2} = 64

⇒ r = √64 = 8cm

∴ Radius of the base of the cone is 8cm.

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