Choose the correct answer of the following question:
Question:

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

Solution:

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).