A copper wire, 3 mm in diameter, is wound 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
Answers
Answer:
ɪᴛ ɪs ᴀssᴜᴍᴇᴅ ᴛʜᴀᴛ ᴏɴᴇ ʀᴏᴜɴᴅ ᴏғ ᴄᴏᴘᴘᴇʀ ᴡɪʀᴇ ᴡɪʟʟ ᴄᴏᴠᴇʀ 3 ᴍᴍ ᴏʀ 0.3 ᴄᴍ ʜᴇɪɢʜᴛ ᴏғ ᴄʏʟɪɴᴅᴇʀ.
ɴᴜᴍʙᴇʀ ᴏғ ʀᴏᴜɴᴅs = ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴄʏʟɪɴᴅᴇʀ/ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴡɪʀᴇ
= 12/0.3
= 40 ʀᴏᴜɴᴅs
ɴᴏᴡ,
ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ᴡɪʀᴇ ʀᴇϙᴜɪʀᴇᴅ ɪɴ ᴏɴᴇ ʀᴏᴜɴᴅ = ᴄɪʀᴄᴜᴍғᴇʀᴇɴᴄᴇ ᴏғ ᴛʜᴇ ʙᴀsᴇ ᴏғ ᴛʜᴇ ᴄʏʟɪɴᴅᴇʀ
ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴄʏʟɪɴᴅᴇʀ = 10 ᴄᴍ, sᴏ ᴛʜᴇ ʀᴀᴅɪᴜs = 5 ᴄᴍ.
ᴄɪʀᴄᴜᴍғᴇʀᴇɴᴄᴇ = 2πʀ
= 2*π*5
ʟᴇɴɢᴛʜ ᴏғ ᴡɪʀᴇ ʀᴇϙᴜɪʀᴇᴅ ɪɴ ᴏɴᴇ ʀᴏᴜɴᴅ = 10π
ʟᴇɴɢᴛʜ ᴏғ ᴡɪʀᴇ ʀᴇϙᴜɪʀᴇᴅ ɪɴ 40 ʀᴏᴜɴᴅs = 10π*40
= 400*22/7
= 8800/7
ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ᴡɪʀᴇ = 1257.14 ᴄᴍ
ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ᴡɪʀᴇ = 0.3/2 = 0.15 ᴄᴍ
ᴠᴏʟᴜᴍᴇ ᴏғ ᴡɪʀᴇ = ᴀʀᴇᴀ ᴏғ ᴄʀᴏss sᴇᴄᴛɪᴏɴ ᴏғ ᴡɪʀᴇ × ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ᴡɪʀᴇ
= π*ʀ² × 12.57
22/7 × (0.15)² × 1257.14
ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ᴡɪʀᴇ = 88.898 ᴄᴍ³
ᴍᴀss = ᴅᴇɴsɪᴛʏ × ᴠᴏʟᴜᴍᴇ
= 8.88 × 88.898
ᴍᴀss = 789.41 ɢᴍ
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Answer:
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