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.

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Updated on: 10-Oct-2022

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