Question

The numbers of coins of $1.5$ cm in diameter and $0.2$ cm thick, to be melted to form a right circular cylinder of height $10$ cm and diameter $4.5$ cm is:

• A. $150$
• B. $250$
• C. $450$
• D. $500$

Answer 1

Answer: (C)

$450$

Let $n$ be the number of $1.5$ cm diameter coins required to form a right circular cylinder of height $10$ cm and diameter $4.5$ cm.

Now,

Volume of right circular cylinder $=n\times$ volume of $1.5$ cm diameter coin.

Therefore,

$n=\frac{\pi {\left(\frac{4.5}{2}\right)}^2\times 10}{\pi {\left(\frac{1.5}{2}\right)}^2\times \frac{2}{10}}$

$=\frac{45\times 45}{20\times 20}\times \frac{10\times 20\times 20\times 10}{15\times 15\times 2}$

$=9\times 10\times 5$

$=450$