Question

If n coins each of diameter $1.5cm$ and thickness $0.2cm$ are melted and a right circular cylinder of height $10cm$ and diameter $4.5cm$ is made, then $n=$

• A. $336$
• B. $450$
• C. $512$
• D. $545$

Answer 1

The correct option is B $450$

A coin is in the shape of a cylinder.

Volume of a cylinder of radius $R$ and height $h$ $=\pi R^{2}h$

Radius of the coin $=\frac{Diameter}{2}=\frac{1.5}{2}cm$

Radius of the new cylinder formed $=\frac{Diameter}{2}=\frac{4.5}{2}cm$

Since $n$ coins are melted and a cylinder is formed out of it,

Therefore,

$n$ $\times$ (Volume of one coin) $=$ Volume of the new cylinder

$n\times \pi \times {\left(\frac{1.5}{2}\right)}^2\times 0.2=\pi \times {\left(\frac{4.5}{2}\right)}^2\times 10$

$\therefore n=450$Coins