Find the number of metallic circular discs wi | vedclass

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Question

(A) metallic circular disc is essentially a thin right circular cylinder.For the metallic circular disc:Diameter $= 1.5\, cm$,so radius $(r) = \frac{1

Vedclass · Accepted Answer

$450$

Vedclass · Answer

(A) metallic circular disc is essentially a thin right circular cylinder.For the metallic circular disc:Diameter $= 1.5\, cm$,so radius $(r) = \frac{1.5}{2} = 0.75\, cm$.Height $(h) = 0.2\, cm$.Volume of one disc $= \pi r^2 h = \pi 	imes (0.75)^2 	imes 0.2 = \pi 	imes 0.5625 	imes 0.2 = 0.1125\pi\, cm^3$.For the large right circular cylinder:Diameter $= 4.5\, cm$,so radius $(R) = \frac{4.5}{2} = 2.25\, cm$.Height $(H) = 10\, cm$.Volume of the cylinder $= \pi R^2 H = \pi 	imes (2.25)^2 	imes 10 = \pi 	imes 5.0625 	imes 10 = 50.625\pi\, cm^3$.Number of discs required $= \frac{	ext{Volume of cylinder}}{	ext{Volume of one disc}} = \frac{50.625\pi}{0.1125\pi} = \frac{506250}{1125} = 450$.Thus,the required number of metallic circular discs is $450$.

Find the number of metallic circular discs with $1.5\, cm$ base diameter and height $0.2\, cm$ that must be melted to form a right circular cylinder of height $10\, cm$ and diameter $4.5\, cm$.

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