Question

The diameter of the base of a cylindrical metal block is 8.8cm and its height is 0.4m. How many discs of diameter 4.4cm and hieght 0.2cm can be formed from this metal block?​

Answer 1

Solution :

Diameter of the base of a cylindrical block d = 8.8 cm

Radius of the cylindrical block r = d/2 = 8.8/2 = 4.4 cm

Height of the cylindrical block h = 0.4 cm

All other dimensions are in cm but height is in m, so let's convert in into cm

We know that

1 m = 100 cm

So, 0.4 m = 0.4 * 100 = 40 cm

i.e h = 40 cm

Diameter of the discs d' = 4.4 cm

Radius of the discs r' = d'/2 = 4.4/2 = 2.2 cm

Height of the disc h' = 0.2 cm

Let the number of discs that can form a cylindrical block be n

Here

n * Volume of the disc = Volume of the cylindrical block

⇒ n * π * r'² * h' = πr²h

⇒ n * r'² * h' = r² * h

Substituting the values

⇒ n * (2.2)² * 0.2 = (4.4)² * 40

⇒ n * 4.84 * 0.2 = 19.36 * 40

⇒ n = (19.36 * 40) / (4.84 * 0.2)

⇒ n = (193.6 * 4) / (4.84 * 0.2)

⇒ n = (193.6 * 20)/ 4.84

⇒ n = (1936 * 2)/4.84

⇒ n = 1936/2.42

⇒ n = 193600/242

⇒ n = 800

Hence, 800 discs are required to form a cylindrical block.

Answer 2

Given :---

• diameter of base of cylinder = 8.8cm
• height of cylinder = 0.4m
• diameter of disc = 4.4cm
• height of disc = 0.2cm

To Find :------

• How many disc can be Formed from this metal block cylinder ?

Formula used :----

• Volume of cylinder = πr²h
• radius = diameter /2
• 1m = 100cm
• No. of disc required = Volume of cylinderical block/volume of one disc

solution :------

Radius of cylinderical block = 8.8/2 = 4.4cm

Height of cylinderical block = 0.4×100 = 40cm

Now,

Radius of disc = 4.4/2 = 2.2cm

Height = 0.2cm .

Now , let n number of disc will be formed from cylinderical metal block .

so,

$n = \frac{ \cancel\pi \times (4.4)^{2} \times 40 }{ \cancel\pi \times {(2.2)}^{2} \times 0.2} \\ \\ n = \frac{\cancel4.4 \times\cancel 4.4 \times 40 \times 10}{\cancel2.2 \times\cancel 2.2 \times \cancel2} \: \\ \\ n = 2 \times 40 \times 10 \\ \\ n = 800$

So, 800 disc would be made From this metal Block .

(Hope it Helps you)