Question

4. A solid metal cylinder of radius 14 cm and height 21
cm is melted down and recast into smaller cylinder
of radius 3.5 cm and height 2.8 cm. Calculate the
number of
oder​

Answer 1

Given :-

▪ A solid metal cylinder of radius , R = 14 cm and height H = 21 cm is melted down and recast into smaller cylinders of radius r = 3.5 cm , and height h = 2.8 cm

To Find :-

▪ Number of smaller cylinders.

Solution :-

Since the big cylinder is melted and recast into smaller cylinders. Then the volume of the big cylinder will be equal to the total volume of all the smaller cylinders.

Big Cylinder :

We have,

• Radius, R = 14 cm
• Height, H = 21 cm

So,

⇒ Volume of cylinder = πR²H

⇒ V = 22/7 × 14 × 14 × 21 [ take, π = 22 / 7 ]

⇒ V = 22 × 2 × 14 × 21

⇒ V = 44 × 294

⇒ V = 12936 cm³

Now,

Smaller Cylinder :

We are given,

• Radius, r = 3.5 cm
• Height, h = 2.8 cm

So,

⇒ Volume of one smaller cylinder = πr²h

⇒ v = 22/7 × 3.5 × 3.5 × 2.8 [ take, π = 22/7 ]

⇒ v = 22 × 0.5 × 3.5 × 2.8

⇒ v = 11 × 9.8

⇒ v = 107.8

Let there be n number of smaller cylinders. As discussed above, Volume of all the smaller cylinders is equal to the volume of the big cylinder.

⇒ V = n × v

⇒ 12936 = n × 107.8

⇒ n = 12936 / 107.8

⇒ n = 120

Hence, There are 120 smaller cylinder recast from the bigger cylinder.