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.

Answer 1

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.