Question:
The number of solid spheres, each of diameter 6 cm that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm, is
(a) 3
(b) 4
(c) 5
(d) 6
Solution:
Here,
Diameter of sphere = 6 cm
Radius of sphere
$=\frac{6}{2} \mathrm{~cm}$
$=3 \mathrm{~cm}$
Volume of the sphere
$=\frac{4}{3} \pi r^{3}$
$=36 \pi$ $........(i)$
Now,
Diameter of cylinder = 4 cm
Radius of cylinder $=\frac{4}{2} \mathrm{~cm}$
$=2 \mathrm{~cm}$
Height of the cylinder = 45 cm
Then,
Volume of the cylinder
$=\pi r^{2} h$
$=\pi \times 2 \times 2 \times 45$
$=180 \pi$
The number of solid sphere
$=\frac{\text { volume of cylinder }}{\text { volume of sphere }}$
$=5$
The number of solid sphere is 5.
Hence, the correct answer is choice (c).