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. $6$

Answer 1

The correct option is C $5$

Volume of the cylinder $=\pi r^{2}h=\pi {\left(2\right)}^2\left(45\right)cc$

Volume of the sphere $=\frac{4}{3}\pi R^3=\frac{4}{3}\pi {\left(3\right)}^3$

Say we need $n$ such spheres

Then,

Volume of the cylinder$=n\times$volume of the sphere

$=>4\times 45\times \pi =n\times \frac{4}{3}\pi \times 27=>n=5$