• The radius of a piece of wire is decreased to one -half.If the volume remains the same , then the length will increase
• 2 times
• 3 times
• 4 times
• 5 times

Show the explanation plz

Let the original radius and length of the piece of wire be r and h respectively and the radius and length of the new piece of wire be R and H respectively.

According to the question

R = r/2

and volume is the same

⇒ πr²h = πR²H

⇒ r²h = R²H

⇒ r²h = (r/2)²H

⇒ r²h = r²H/4

⇒ h = 4h

Hence, length will increase 4 times.