Question

The diameter of a metallic sphere is 6 cm It is melted and drawn into a wire having diameter of the cross section is 0.2 cm find the length of the wire

Answer 1

volume of sphere = volume of wire

4/3 X22/7X 3 X 3 X 3 =22/7X 0.1 X 0.1 X h

h = (4 X 3 X 3)/(0.1 X 0.1)

h= 3600 cm

therefore, the length of the wire is 36m.

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Answer 2

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$\huge\fcolorbox{black}{aqua}{Solution:-}$

✒ ᴀɴsᴡᴇʀ:-

⛄ ʜ = 36 ᴍᴇᴛʀᴇs.

✒ sᴛᴇᴘ-ʙʏ-sᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

⛄ᴡᴇ ʜᴀᴠᴇ,

ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴍᴇᴛᴀʟʟɪᴄ sᴘʜᴇʀᴇ = 6 ᴄᴍ

ᴛʜᴇʀᴇғᴏʀᴇ,

ʀᴀᴅɪᴜs ᴏғ ᴍᴇᴛᴀʟʟɪᴄ sᴘʜᴇʀᴇ = 3 ᴄᴍ

ᴀʟsᴏ, ᴡᴇ ʜᴀᴠᴇ

ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴄʀᴏss-sᴇᴄᴛɪᴏɴ ᴏғ ᴄʏʟɪɴᴅʀɪᴄᴀʟ ᴡɪʀᴇ = 0.2 ᴄᴍ.

ᴛʜᴇʀᴇғᴏʀᴇ,

ʀᴀᴅɪᴜs ᴏғ ᴄʀᴏss-sᴇᴄᴛɪᴏɴ ᴏғ ᴄʏʟɪɴᴅʀɪᴄᴀʟ ᴡɪʀᴇ = 0.1 ᴄᴍ.

ʟᴇᴛ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ᴡɪʀᴇ ʙᴇ ʜ ᴄᴍ. sɪɴᴄᴇ ᴍᴇᴛᴀʟʟɪᴄ sᴘʜᴇʀᴇ ɪs ᴄᴏɴᴠᴇʀᴛᴇᴅ ɪɴᴛᴏ ᴀ ᴄʏʟɪɴᴅʀɪᴄᴀʟ sʜᴀᴘᴇᴅ ᴡɪʀᴇ ᴏғ ʟᴇɴɢᴛʜ ʜ ᴄᴍ.

ᴛʜᴇʀᴇғᴏʀᴇ,

ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ᴍᴇᴛᴀʟ ᴜsᴇᴅ ɪɴ ᴡɪʀᴇ = ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ sᴘʜᴇʀᴇ.

=> π × (0.1)² × ʜ = 4/3 × π × 3³

=> π × [1/10]² × ʜ = 4/3 × π × 27

=> π × 1/100 × ʜ = 36 π

=> ʜ = 36π × 100/ π ᴄᴍ

=> ʜ = 3600 ᴄᴍ

ᴏʀ

☞ ʜ = 36 ᴍᴇᴛʀᴇs.

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