Question

A rectangular circular metal sheet 48cm in diameter and 2cm thick is melted and recast into a cylindrical bar 6cm in diameter how long is the bar

Answer 1

Given:

A circular metal sheet of 48 cm in diameter and 2 cm thick is melted and recast into a cylindrical bar of 6 cm in diameter

To find: the length of the bar

Step-by-step explanation:

Let us find the volume of the circular metal sheet first.

Given, the diameter of the circle is 48 cm

Then its radius is (48 ÷ 2) cm = 24 cm

Thus its area is π × 24² cm² = 576π cm²

Now the volume of the circular metal sheet

= area of the circle × thickness of the metal

= 576π × 2 cm³

= 1152π cm³

Finding length of the cylindrical bar.

Given, the diameter of the circle is 6 cm

Then its radius is (6 ÷ 2) cm = 3 cm

Thus its area is π × 3² cm² = 9π cm²

Let, the length of the cylindrical bar be h cm

Then its volume

= area of the base × length

= 9π × h cm³

Equating volumes of the metal sheet and the bar.

Here we understand that the volume of the circular metal sheet is equal to the volume of the cylindrical bar.

Thus, 9π × h = 1152π

➾ 9 × h = 1152

➾ h = 1152 ÷ 9

➾ h = 128

Answer:

Hence the the cylindrical bar is 128 cm long.

Answer 2

Answer:  Length of the cylindrical bar =128 cm

Step-by-step explanation:

Given:

Diameter of circular sheet(D)= 48 cm

thickness of circular sheet(t)=2 cm

Cylindrical bar diameter= 6 cm

Now,

area of circular sheet(A)=π$R^{2}$

A=π×$24^{2}$

A=576π cm²

hence,

volume of circular sheet=A×t

V=576π×2

V=1152π cm³

Let,

L=length of cylindrical bar

Volume of cylindrical bar=π(3)²L

on melting

Volume of circular sheet=volume of cylindrical bar

1152π=π(3)²L

L=128 cm

Therefore,

length of the cylindrical bar is 128 cm