Question

Question 14
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 = 1.5cm
$\therefore$ Radius of metallic circular disc $=\frac{1.5}{2}cm[\because diameter=2\times radius]$
And height of metallic circular disc i.e = 0.2 cm
$\therefore$ Volume of a circular disc $=\pi \times (Radius{)}^2\times Height$
$=\pi \times {\left(\frac{1.5}{2}\right)}^2\times 0.2=\frac{\pi }{4}\times 1.5\times 1.5\times 0.2$
Now, height of a right circular cylinder (h) = 10 cm
And diameter of a right circular cylinder = 4.5 cm
$\Rightarrow$ Radius of a right circular cylinder $\left(r\right)=\frac{4.5}{2}cm$
$\therefore$ Volume of right circular cylinder $=\pi r^{2}h$
$\pi {\left(\frac{4.5}{2}\right)}^2\times \frac{\pi }{4}\times 4.5\times 4.5\times 10$
$\therefore$ Number of metallic circular disc = ​$\frac{Volumeofarightcicularcylinder}{Volumeofametalliccirculardisc}$
$=\frac{\pi }{4}\times 4.5\times 4.5\times 10\frac{\pi }{4}\times 1.5\times 1.5\times 0.2=\frac{3\times 3\times 10}{0.2}=\frac{900}{2}=450$
Hence, the required number of metallic circular disc is 450.