 Hello and welcome to the session I am Deepika here. Let's discuss the question which says a copper wire 3 mm in diameter is bound about a cylinder whose length is 12 cm and diameter 10 cm so as to cover the curved surface of the cylinder. Find the length and mass of the wire assuming the density of copper to be 8.88 g per cm cube. Now we know that volume of a cylinder is equal to pi r square h where r is the radius of the base of this cylinder and h is the height of this cylinder. And again mass is equal to density into volume. So this is a key idea behind our question. We will take the help of this key idea to solve the above question so let's start the solution. According to the question a copper wire 3 mm in diameter is bound about a cylinder whose length is 12 cm. Hence we are given diameter of copper wire is equal to 3 mm and this is equal to 3 by 10 cm because 1 cm is equal to 10 mm that is 1 mm is equal to 1 by 10 cm therefore 3 mm is equal to 3 by 10 cm. And length of this cylinder equal to 12 cm. Now the wire is bound around this cylinder so one round of wire covers 3 by 10 cm in thickness of the surface of cylinder length 12 cm therefore number of rounds to cover 12 cm is equal to 12 upon 3 upon 10 that is this is equal to 12 into 10 over 3. So in 40 rounds a copper wire can bound about a cylinder whose length is 12 cm. Now the diameter of the cylinder is is given to us 10 cm so therefore radius of this cylinder is equal to 5 cm let us convert this into meter so we have this is equal to 5 upon 100 meters and this is equal to 0.05 meter. Because 1 meter is equal to 100 cm. Now we want to find the length of wire so as to cover the curved surface of this cylinder so the length of wire for one round to cover the curved surface of this cylinder is equal to 2 pi r therefore length of wire for 40 rounds is equal to 2 pi r into 40 let us take pi is equal to 3.14 so this is equal to 2 into 3.14 into r is 0.05 meter into 40 meter and this is equal to 12.56 meter. Now we have to find the mass of the wire and according to our key idea mass is equal to density into volume density is given to us it is 8.88 gram per centimeter cube so let us first find out the volume of cylinder. Now radius of the wire is given to us and it is 3 pi 2 millimeter because diameter is 3 millimeter and this is equal to 1.5 millimeter let us convert this into centimeter so we have this is equal to 1.5 upon 10 centimeter and this is equal to 0.15 centimeter. Now length of wire for 40 rounds is 12.56 meter that is height is 12.56 meter and this is equal to 12.56 centimeter therefore volume of this cylinder is equal to pi r square h take pi is equal to 3.14 so we have 3.14 into 0.15 into 0.15 into 12.56 centimeter cube and this is equal to 88.73 centimeter cube. Now according to our key idea mass is equal to density into volume. Now density is given to us 8.88 gram per centimeter cube so this is equal to 8.88 into volume is 88.73 gram per centimeter cube and this is equal to 787.979 grams per centimeter cube and this is again equal to 0.780 kilogram per centimeter cube. Hence the answer for the above question is the length of the wire is 12.56 meter and mass of the wire is 0.780 kilogram per centimeter cube. I hope the solution is clear to you. Bye and take care.