The number of coins,each of radius 0.75, cm a | vedclass

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Question

(A) Let the number of required coins be $x$.The volume of a single coin (which is a cylinder) is given by $V = \pi r^2 h$.For each coin,$r = 0.75\, cm

Vedclass · Accepted Answer

$640$

Vedclass · Answer

(A) Let the number of required coins be $x$.The volume of a single coin (which is a cylinder) is given by $V = \pi r^2 h$.For each coin,$r = 0.75\, cm$ and $h = 0.2\, cm$.Total volume of $x$ coins $= x 	imes \pi 	imes (0.75)^2 	imes 0.2$.The volume of the target right circular cylinder is $V = \pi R^2 H$.Here,$R = 3\, cm$ and $H = 8\, cm$.Volume of cylinder $= \pi 	imes (3)^2 	imes 8 = \pi 	imes 9 	imes 8 = 72\pi\, cm^3$.Equating the volumes:$x 	imes \pi 	imes (0.75)^2 	imes 0.2 = 72\pi$$x 	imes (0.5625) 	imes 0.2 = 72$$x 	imes 0.1125 = 72$$x = \frac{72}{0.1125}$$x = \frac{720000}{1125} = 640$.Thus,the number of coins required is $640$.

The number of coins,each of radius $0.75\, cm$ and thickness $0.2\, cm$,to be melted to make a right circular cylinder of height $8\, cm$ and radius $3\, cm$ is:

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