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Find the number of metallic circular discs with $ 1.5 \mathrm{~cm} $ base diameter and of height $ 0.2 \mathrm{~cm} $ to be melted to form a right circular cylinder of height $ 10 \mathrm{~cm} $ and diameter $ 4.5 \mathrm{~cm} $
Given:
Diameter of each metallic circular disc $=1.5\ cm$
Height of each metallic circular disc $=0.2\ cm$
Height of right circular cylinder $=10\ cm$
Diameter of right circular cylinder $=4.5\ cm$
To do:
We have to find the number of metallic circular discs to be melted.
Solution:
Radius of each circular disc $=\frac{1.5}{2}\ cm$
This implies,
Volume of each circular disc $= \pi r^2 h$
$=\pi \times (\frac{1.5}{2})^{2} \times 0.2$
$=\frac{\pi}{4} \times 1.5 \times 1.5 \times 0.2$
Radius of the right circular cylinder $R=\frac{4.5}{2} \mathrm{~cm}$
This implies,
Volume of the right circular cylinder $=\pi R^{2} H$
$=\pi(\frac{4.5}{2})^{2} \times 10$
$=\frac{\pi}{4} \times 4.5 \times 4.5 \times 10$
Number of metallic circular discs $=\frac{\text { Volume of the right circular cylinder }}{\text { Volume of each circular disc }}$
$=\frac{\frac{\pi}{4} \times 4.5 \times 4.5 \times 10}{\frac{\pi}{4} \times 1.5 \times 1.5 \times 0.2}$
$=\frac{3 \times 3 \times 10}{0.2}$
$=\frac{900}{2}$
$=450$
The number of metallic circular discs to be melted is 450.