 Hello and welcome to the session. In this session we discuss the following question which says, a piece of a ductile metal is in the form of a cylinder of diameter 2 cm and length 11 cm. It is drawn out into a wire of diameter 2 mm. What will be the length of the wire so obtained? First let's recall the formula for the volume of the cylinder. This is equal to pi r square h, r is the radius of the cylinder, h is the height of the cylinder. This is the key idea to be used in this question. Now let's move on to the solution. We are given the diameter of the cylinder is equal to 2 cm. So this means we have the radius of the cylinder is equal to 2 upon 2 cm equal to 1 cm. And we are also given the length or we can also say the height of the cylinder 11 cm. We take the radius of the cylinder as r, height of the cylinder as h. So now volume of the cylinder is equal to pi r square into h cm cube. That is we have volume of cylinder is equal to 11 pi cm cube. Now this cylinder is drawn into a wire and we are given the diameter of the wire is equal to 2 mm. That is the radius of the wire say r1 is equal to 2 upon 2 mm equal to 1 mm. We know that 10 mm is equal to 1 cm. That is 1 mm is equal to 1 upon 10 cm. So this means that the radius of the wire is equal to 0.1 cm. Now we take let the length of the wire obtained be equal to h1 cm. So the volume of the wire obtained is equal to pi r1 square that is 0.1 square into h1 cm cube. Now since the cylinder is drawn into the wire so the volume of cylinder would be equal to the volume of the wire obtained. This means volume of cylinder that is 11 pi is equal to volume of the wire that is pi into 0.1 square into h1. That is we have 11 pi is equal to h1 into 0.01 into pi. Now here pi and pi gets cancelled and we get h1 is equal to 11 upon 0.01 cm. That is we get h1 is equal to 1100 cm. That is the length of the wire obtained is equal to 1100 cm. So our final answer is 1100 cm. This completes the session. Hope you have understood the solution for this question.