Choose the correct answer of the following question:
The number of solid spheres, each of diameter 6 cm, that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is
(a) 2 (b) 4 (c) 5 (d) 6
We have,
Radius of the spher, $r=\frac{6}{2}=3 \mathrm{~cm}$,
Height of the cylinder, $H=45 \mathrm{~cm}$ and
Radius of the cylinder, $R=\frac{4}{2}=2 \mathrm{~cm}$
Now,
The number of sphere that can be made $=\frac{\text { Volume of the cylinder }}{\text { Volume of the sphere }}$
$=\frac{\pi R^{2} H}{\left(\frac{4}{3} \pi r^{3}\right)}$
$=\frac{3 R^{2} H}{4 r^{3}}$
$=\frac{3 \times 2 \times 2 \times 45}{4 \times 3 \times 3 \times 3}$
$=5$
Hence, the correct answer is option (c).