Question

The curved surface of a cylinder is $1000c{m}^2$. A wire of diameter $5mm$ is wound around it, so as to cover it completely. What is the length of the wire used?

• A. $22m$
• B. $20m$
• C. $18m$
• D. None of these

Answer 1

Answer: (B)

$20m$

$1000c{m}^2=2\pi \times radius\times height$
Let the no. of turns the wire had made on the surface be $n$.
For $n$ turns, the wire should make upto $5n$ mm or $0.005n$ m height

Since the wire should completely cover the cylinder,
$\therefore$ Height of cylinder $=0.005n$ m
Let the length of wire needed be $l$m
$l=2\pi \times radius\times n$
$\frac{l}{n}=2\pi \times radius$
$1000c{m}^2=0.1m^2=2\pi \times radius\times height$
$0.1=\left(\frac{l}{n}\right)\times 0.005n$
$l=\frac{0.1}{0.005}=20m$