Find the number of metallic circular disc with 1.5 cm

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

$\therefore$ Radius of metallic circular disc $=\frac{1.5}{2} \mathrm{~cm}$ $[\because$ diameter $=2 \times$ radius $]$

and heiaht of metallic circular disc $i . e .,=0.2 \mathrm{~cm}$

$\therefore \quad$ Volume of a circular disc $=\pi \times(\text { Radius })^{2} \times$ 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 $(h)=10 \mathrm{~cm}$

and diameter of a right circular cylinder $=4.5 \mathrm{~cm}$

$\Rightarrow$ Radius of a right circular cylinder $(r)=\frac{4.5}{2} \mathrm{~cm}$.

$\therefore \quad$ Volume of right circular cylinder $=\pi r^{2} h$

$=\pi\left(\frac{4.5}{2}\right)^{2} \times 10=\frac{\pi}{4} \times 4.5 \times 4.5 \times 10$

$\therefore$ Number of metallic circular disc $=\frac{\text { Volume of a right circular cylinder }}{\text { Volume of a metallic circular disc }}$

$=\frac{\frac{\pi}{4} \times 4.5 \times 4.5 \times 10}{\frac{\pi}{4} \times 1.5 \times 1.5 \times 0.2}$

$=\frac{3 \times 3 \times 10}{0.2}=\frac{900}{2}=450$

Hence, the required number of metallic circular disc is 450 .

 

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now