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Mathematics

A solid metallic sphere of radius 16 cm is melted to form small identical spheres each of diameter 4 cm. The number of spheres formed is :

  1. 64

  2. 252

  3. 512

  4. 1024

Mensuration

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Answer

Given,

A solid metallic sphere of radius 16 cm is melted to form small identical spheres each of diameter 4 cm.

Larger metallic ball sphere radius (R) = 16 cm

Radius of smaller metallic sphere (r) = 42\dfrac{4}{2} = 2 cm

Let no. of smaller spheres formed be n.

∴ Volume of larger metallic ball = n × Volume of smaller metallic ball

⇒43πR3=n×43πr3⇒n=43πR343πr3⇒n=R3r3⇒n=16323⇒n=40968=512.\Rightarrow \dfrac{4}{3}πR^3 = n \times \dfrac{4}{3}πr^3 \\[1em] \Rightarrow n = \dfrac{\dfrac{4}{3}πR^3}{\dfrac{4}{3}πr^3} \\[1em] \Rightarrow n = \dfrac{R^3}{r^3} \\[1em] \Rightarrow n = \dfrac{16^3}{2^3} \\[1em] \Rightarrow n = \dfrac{4096}{8} = 512.

Hence, Option 3 is the correct option.

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