Question

Small spherical balls, each of diameter $0.6$ cm, are formed by melting a solid sphere of radius $3$ cm. Find the number of balls thus obtained.

Answer 1

Given radius of large sphere = 3 cm

Volume of large sphere = $\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times (3{)}^3$

[Volume = $36\pi c{m}^3$]

Now small spherical balls are to be made from large sphere having radius = $0.3cm$

Volume of 1 small spherical ball = $\frac{4}{3}\pi (0.3{)}^3$

Volume = $36\pi \times {10}^{-3}c{m}^3$

Now total number of balls are to be made.

$=\frac{36\pi }{36\pi \times {10}^{-3}}=1000$

Hence 1000 balls can be made using larger metallic sphere.