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An oil funnel made of tin sheet consists of a
10 cm long cylindrical portion attached to a
frustum of a cone. If the total height is 22 cm,
diameter of the cylindrical portion is 8 cm and
the diameter of the top of the funnel is 18 cm,
find the area of the tin sheet required to make
the funnel (see Fig. 13.25)
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Answers
Hey your answer is in the given attachment
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ʟᴇᴛ ʀ 1 ᴀɴᴅ ʀ 2 ( ʀ 1 > ʀ 2) ʙᴇ ᴛʜᴇ ʀᴀᴅɪɪ ᴏғ ᴇɴᴅs ᴏғ ᴛʜᴇ ғʀᴜsᴛᴜᴍ ᴏғ ᴀ ᴄᴏɴᴇ.
sᴜᴘᴘᴏsᴇ ʟ, ʜ ᴀɴᴅ ʜ ʙᴇ ᴛʜᴇ sʟᴀɴᴛ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ғʀᴜsᴛᴜᴍ, ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ғʀᴜsᴛᴜᴍ ᴀɴᴅ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴄʏʟɪɴᴅᴇʀ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.
ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛᴏᴘ ᴏғ ᴛʜᴇ ғʀᴜsᴛᴜᴍ, 2ʀ 1 = 18 ᴄᴍ
∴ ʀ 1 = 9 ᴄᴍ.
ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ʙᴏᴛᴛᴏᴍ ᴏғ ᴛʜᴇ ғʀᴜsᴛᴜᴍ, 2ʀ 2 = 8 ᴄᴍ
∴ ʀ 2 = 4 ᴄᴍ
ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ғʀᴜsᴛᴜᴍ = ᴛᴏᴛᴀʟ ʜᴇɪɢʜᴛ ᴏғ ғᴜɴɴᴇʟ – ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴄʏʟɪɴᴅᴇʀ = 22 ᴄᴍ – 10 ᴄᴍ = 12 ᴄᴍ
sʟᴀɴᴛ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ғʀᴜsᴛᴜᴍ, ʟ
= ʜ 2 + ( ʀ 1 - ʀ 2 ) 2
= (12 ᴄᴍ) 2 + (9 ᴄᴍ - 4 ᴄᴍ) 2
= 144 ᴄᴍ 2 + 25 ᴄᴍ 2
= 169 ᴄᴍ 2
= 13 ᴄᴍ
ᴄᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ᴛʜᴇ ᴏɪʟ ғᴜɴɴᴇʟ = π( ʀ 1 + ʀ 2)ʟ + 2πʀ 2ʜ
∴ ᴀʀᴇᴀ ᴏғ ᴛɪɴ sʜᴇᴇᴛ ʀᴇϙᴜɪʀᴇᴅ ᴛᴏ ᴍᴀᴋᴇ ᴛʜᴇ ғᴜɴɴᴇʟ
= π( ʀ 1 + ʀ 2)ʟ + 2πʀ 2 ʜ
= 22 7 (9 ᴄᴍ + 4 ᴄᴍ) × 13 ᴄᴍ + 2 × 22 7 × 4 ᴄᴍ × 10 ᴄᴍ
= 22 7 (13 × 13 ᴄᴍ 2 + 80 ᴄᴍ 2 )
= 22 7 × ( 169 ᴄᴍ 2 + 80 ᴄᴍ 2 )
= 22 7 × 249 ᴄᴍ 2
= 782.6 ᴍ 2
ᴛʜᴜs, ᴛʜᴇ ᴀʀᴇᴀ ᴏғ ᴛɪɴ sʜᴇᴇᴛ ʀᴇϙᴜɪʀᴇᴅ ᴛᴏ ᴍᴀᴋᴇ ᴛʜᴇ ᴏɪʟ ғᴜɴɴᴇʟ ɪs 782.6 ᴄᴍ2.
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