Question

The radius of the wire is decreased to 1/3rd. If the volumes remains same, length will be increased by?​

Answer 1

GivEn:-

• The radius of the wire is decreased to 1/3rd.

To find:-

• If the volumes remains same, length will be increased by?

Solution:-

As we know that,

The wire is in shape of cylinder.

Let's the radius of the original cylinder = r cm

Let's the height of the original cylinder = h cm

So, Volume of original wire = πr²h

New radius after decrease = r/3

Let's the new height = H cm

So, Volume of wire after decreasing radius = π(r/3)²H

Given that,

The Volume remains same,

Therefore,

→ πr²h = π(r/3)²H

→ πr²h = π(r²/9)H

Cancelling π from both sides:-

→ r²h = (r²/9)H

→ 9r²h = r²H

Now, Cancelling "r²" from both sides:-

→ 9h = H

Hence, The height is increased by 9 times.

________________________

Answer 2

Given :

• The radius of the wire is decreased to 1/3rd.

To Find :

• If the volumes remains same, length will be increased by?

Solution :

Let the height of original cylinder = r cm and height = h cm.

Original volume = πr²h

New radius after decrease = r/3

Let the new height be H

➩ πr²h = π(r/3)²Hh

➩ H = 9

Hence, the height become 9 times.