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Question
Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Solution
Given that, lots of metallic circular disc to be melted to form a right circular cylinder.
Here, a circular disc work as a circular cylinder.
Base diameter of metallic circular disc = 1.5 cm
∴ Radius of metallic circular disc = `1.5/2` cm ...[∵ diameter = 2 × radius]
And height of metallic circular disc i.e., = 0.2 cm
∴ Volume of a circular disc
= π × (Radius)2 × Height
= `pi xx (1.5/2)^2 xx 0.2`
= `pi/4 xx 1.5 xx 1.5 xx 0.2`
Now, height of a right circular cylinder (h) = 10 cm
And diameter of a right circular cylinder = 4.5 cm
⇒ Radius of a right circular cylinder (r) = `4.5/2` cm
∴ Volume of right circular cylinder
= πr2h
= `pi(4.5/2)^2 xx 10`
= `pi/4 xx 4.5 xx 4.5 xx 10`
∴ Number of metallic circular disc
= `"Volume of a right circular cylinder"/"Volume of a metallic circular disc"`
= `(pi/4 xx 4.5 xx 4.5 xx 10)/(pi/4 xx 1.5 xx 1.5 xx 0.2)`
= `(3 xx 3 xx 10)/0.2`
= `900/2`
= 450
Hence, the required number of metallic circular disc is 450.
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