How many coins,2 , mm thick and 1.5 , cm in d | vedclass

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Question

(A) Radius of the coin $r = \frac{1.5}{2} = 0.75 \, cm = \frac{3}{4} \, cm$.Thickness of the coin $h = 2 \, mm = 0.2 \, cm = \frac{1}{5} \, cm$.Volume

Vedclass · Accepted Answer

$640$

Vedclass · Answer

(A) Radius of the coin $r = \frac{1.5}{2} = 0.75 \, cm = \frac{3}{4} \, cm$.Thickness of the coin $h = 2 \, mm = 0.2 \, cm = \frac{1}{5} \, cm$.Volume of one coin $= \pi r^2 h = \pi 	imes (\frac{3}{4})^2 	imes \frac{1}{5} = \pi 	imes \frac{9}{16} 	imes \frac{1}{5} = \frac{9\pi}{80} \, cm^3$.Radius of the cylinder $R = \frac{6}{2} = 3 \, cm$.Height of the cylinder $H = 8 \, cm$.Volume of the cylinder $= \pi R^2 H = \pi 	imes (3)^2 	imes 8 = 72\pi \, cm^3$.Number of coins $= \frac{	ext{Volume of the cylinder}}{	ext{Volume of one coin}} = \frac{72\pi}{\frac{9\pi}{80}} = 72 	imes \frac{80}{9} = 8 	imes 80 = 640$.

How many coins,$2 \, mm$ thick and $1.5 \, cm$ in diameter,should be melted in order to form a right circular cylinder with base diameter $6 \, cm$ and height $8 \, cm$?

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