Q. 275.0( 2 Votes )

A. 2 cm

B. 3 cm

C. 4 cm

D. 6 cm

Answer :

Given: A solid metallic cylinder of base diameter 2 cm and height 16 cm.

Twelve solid sphere of the same size are made by melting a solid metallic cylinder .

Let V_{1} be the volume of the cylinder

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

∴ V_{1} = π × 1^{2} × 16 (diameter is 2cm, ∴ radius is 1cm)

Let V_{2} be the volume of the each Sphere.

Volume of the Sphere is given by: × π × r^{3} (where r is the radius of the sphere)

∴ V_{2} = × π × r^{3}

Here,

V_{1} = 12 × V_{2}

∴ π × 1^{2} × 16 = 12 × × π × r^{3}

⇒ r^{3} = = = 1cm

∴ r = ∛1 = 1 cm

∴ Diameter of the Sphere is 2 × r = 2 × 1 = 2cm

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