Find the number of plates 1.5 cm in diameter and 0.2 cm thick that can be fitted completely inside a right circular cylinder of height 10 cm and diameter 4.5 cm.

Given that,  

Plates are fitted completely inside a right circular cylinder 

Diameter of plate$= 1.5 cm$

Thickness of plate$= 0.2 cm$

Height of right circular cylinder $= 10 cm$

Diameter of right circular cylinder$= 4.5 cm$

Radius of right circular cylinder$=2.25 cm$

Volume of right circular cylinder $= \pi r²h$

$=\pi \times 2.25\times 2.25\times 10$

$= \pi \times 0. 5625 \times 0. 2$

$=\frac{405\pi }{8} cm³$

Volume of plate $= \pi r²h$

$=\pi \times 0.75\times 0.75\times 0.2$

$=\pi \times 0.5625\times 0.2$

$=\frac{ 9\pi }{80} 𝑐𝑚³$

$Number of plates =\frac{Volume of right circular cylinder }{Volume of plate }$

$= \frac{{\displaystyle \frac{405\pi }{8 𝑐𝑚³}} }{{\displaystyle \frac{9\pi }{80 𝑐𝑚³}}}$

$= \frac{ 405 \pi }{8} \times \frac{ 80 }{ 9 \pi }$

$= 45 \times 10$

$= 450 plates$

Hence, the number of plates are 450.