Question

Find the number of metallic circular discs with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10cm and diameter 4.5 cm

Answer 1

$\underline{\bold{Solution:-}}$

Let n be the number of metallic disc required to form the right circular cylinder.

Base diameter of disc = 1.5 cm

Radius of disc = 1.5/2 = 0.75 cm

Height of disc = 0.2 cm

Volume of metal in 1 disc
$= \pi {(Radius \: of \: disc)}^{2} \times( Height \: of \: disc) \\ \\ = \pi \times {0.75}^{2} \times 0.2 \\ \\ = 0.1125\pi \: {cm}^{3}$

Volume of metal in n discs
$=n \: 0.1125\pi \: {cm}^{3}$

This metal is melted and then used to form a right circular cylinder.

Volume of metal in cylinder = Volume of metal in n discs ........(1)

Diameter of cylinder = 4.5 cm

Radius of cylinder = 4.5/2 = 2.25 cm

Height of cylinder = 10 cm

Volume of metal in cylinder

$= \pi { (Radius \: of \: cylinder) }^{2} \times( Height \: of \: cylinder) \\ \\ = \pi \times {2.25}^{2} \times 10 \\ \\ = 50.625\pi \: {cm}^{3}$

From eq (1)

Volume of metal in cylinder = Volume of metal in n discs

$50.625\pi \: {cm}^{3} = n \: 0.1125\pi \: {cm}^{3} \\ \\ n = \frac{50.625\pi \: {cm}^{3}}{ 0.1125\pi \: {cm}^{3} } \\ \\ \boxed{n = 450}$

So, 450 such discs will be required to be melt and form a right circular cylinder.

Answer 2

$\huge{\boxed{\boxed{\mathfrak{Hello!!}}}}$

Question
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Find the number of metallic circular discs with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10cm 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

•°•Radius of metallic circular disc = 1.5 / 2 cm

[°•° diameter = 2 × radius]

And height of metallic circular disc is 0.2 cm

•°• Volume of a circular disc:

$= > \pi \: \times {(Radius)}^{2} \: \times Height$

$= > \pi \: \times {( \frac{1.5}{2}) }^{2} \: \times 0.2$

$= > \frac{\pi}{4} \: \times 1.5 \: \times 1.5 \: \times 0.2$

Now,

Height of a right circular cylinder(h) = 10 cm

And,

Diameter of a right circular cylinder(d) = 4.5 cm

=>Radius of a right circular cylinder(r)=4.5/2 cm

•°•Volume of 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 disc:

Volume of a right circular cylinder
--------------------------------------------
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.

$\huge{\underline{\underline{\underline{\undeline{\mathsf{Hope It Helps!!!}}}}}}$