class 9 ch 13 formulas
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ꜰᴀᴄᴛꜱ ᴛʜᴀᴛ ᴍᴀᴛᴛᴇʀ
• ᴛʜʀᴇᴇ ᴍᴇᴀꜱᴜʀᴇꜱ ᴏꜰ ᴄᴇɴᴛʀᴀʟ ᴛᴇɴᴅᴇɴᴄʏ ᴏꜰ ᴜɴɢʀᴏᴜᴘᴇᴅ ᴅᴀᴛᴀ ᴀʀᴇ: (ɪ) ᴍᴇᴀɴ, (ɪɪ) ᴍᴇᴅɪᴀɴ ᴀɴᴅ (ɪɪɪ) ᴍᴏᴅᴇ.
• ᴛᴏᴛᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴏɪᴅ = 2[ʟʙ + ʙʜ + ʟʜ]
• ᴛᴏᴛᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴇ = 6(ꜱɪᴅᴇ)²
• ʟᴀᴛᴇʀᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴏɪᴅ = ᴀʀᴇᴀ ᴏꜰ ᴡᴀʟʟꜱ ᴏꜰ ᴀ ʀᴏᴏᴍ = 2(ʟ + ʙ) × ʜ
• ʟᴀᴛᴇʀᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴇ = 4ᴀ²
• ᴄᴜʀᴠᴇᴅ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴄʏʟɪɴᴅᴇʀ = 2πʀʜ
• ᴛᴏᴛᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄʏʟɪɴᴅᴇʀ = 2πʀ(ʀ + ʜ)
• ᴄᴜʀᴠᴇᴅ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴏɴᴇ = πʀʟ
• ᴛᴏᴛᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴏɴᴇ = πʀ(ʀ + ʟ)
• ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ꜱᴘʜᴇʀᴇ = 4πʀ²
• ᴄᴜʀᴠᴇᴅ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ʜᴇᴍɪꜱᴘʜᴇʀᴇ = 2πʀ²
• ᴛᴏᴛᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ʜᴇᴍɪꜱᴘʜᴇʀᴇ = 3πʀ²
• ᴠᴏʟᴜᴍᴇ ᴏꜰ ᴀ'ᴄᴜʙᴏɪᴅ = ʟ × ʙ × ʜ
• ᴠᴏʟᴜᴍᴇ ᴏꜰ ᴀ ᴄᴜʙᴇ = (ꜱɪᴅᴇ)²
• ᴠᴏʟᴜᴍᴇ ᴏꜰ ᴀ ᴄʏʟɪɴᴅᴇʀ = πʀ²ʀʜ
ꜱᴏʟɪᴅꜱ ᴀɴᴅ ᴛʜᴇɪʀ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀꜱ
ᴛʜᴇ ʙᴏᴅɪᴇꜱ ᴏᴄᴄᴜᴘʏɪɴɢ ꜱᴘᴀᴄᴇ ᴀʀᴇ ᴄᴀʟʟᴇᴅ ꜱᴏʟɪᴅꜱ, ꜱᴜᴄʜ ᴀꜱ ᴀ ᴄᴜʙᴏɪᴅ, ᴀ ᴄᴜʙᴇ, ᴀ ᴄʏʟɪɴᴅᴇʀ, ᴀ ᴄᴏɴᴇ, ᴀ ꜱᴘʜᴇʀᴇ, ᴇᴛᴄ.
ᴛʜᴇꜱᴇ ꜱᴏʟɪᴅꜱ ʜᴀᴠᴇ ᴘʟᴀɴᴇ ᴏʀ ᴄᴜʀᴠᴇᴅ ꜱᴜʀꜰᴀᴄᴇꜱ.
ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴏɪᴅ ᴀɴᴅ ᴀ ᴄᴜʙᴇ
ᴛʜᴇ ᴏᴜᴛᴇʀ ꜱᴜʀꜰᴀᴄᴇ ᴏꜰ ᴀ ᴄᴜʙᴏɪᴅ ɪꜱ ᴍᴀᴅᴇ ᴜᴘ ᴏꜰ ꜱɪx ʀᴇᴄᴛᴀɴɢʟᴇꜱ. ɪꜰ ᴡᴇ ᴛᴀᴋᴇ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴛʜᴇ ᴄᴜʙᴏɪᴅ ᴀꜱ ʟ, ʙʀᴇᴀᴅᴛʜ ᴀꜱ ʙ ᴀɴᴅ ᴛʜᴇ ʜᴇɪɢʜᴛ ᴀꜱ ʜ, ᴛʜᴇɴ
ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴏɪᴅ = 2[ʟʙ + ʙʜ + ʜʟ]
ʟᴇᴛ ᴜꜱ ʀᴇᴄᴀʟʟ ᴛʜᴀᴛ ᴀ ᴄᴜʙᴏɪᴅ ᴡʜᴏꜱᴇ ʟᴇɴɢᴛʜ, ʙʀᴇᴀᴅᴛʜ ᴀɴᴅ ʜᴇɪɢʜᴛ ᴀʀᴇ ᴇQᴜᴀʟ ɪꜱ ᴄᴀʟʟᴇᴅ ᴀ ᴄᴜʙᴇ. ʟᴇᴛ ᴇᴀᴄʜ ᴇᴅɢᴇ ᴏꜰ ᴛʜᴇ ᴄᴜʙᴇ ʙᴇ �ᴀ', ᴛʜᴇɴ
ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴇ = 6ᴀ2
ɴᴏᴛᴇ: ɪ. ꜱᴏᴍᴇᴛɪᴍᴇꜱ ᴀ ᴄᴜʙᴏɪᴅ ᴅᴏᴇꜱ ɴᴏᴛ ʜᴀᴠᴇ ʙᴏᴛᴛᴏᴍ ᴀɴᴅ ᴛᴏᴘ ꜰᴀᴄᴇꜱ. ɪꜱ ᴄᴀʟʟᴇᴅ ᴛʜᴇ ʟᴀᴛᴇʀᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ.
ɪɪ. ʟᴀᴛᴇʀᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴏɪᴅ ɪꜱ 2(ʟ + ʙ)ʜ.
ɪɪɪ. ʟᴀᴛᴇʀᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴇ ɪꜱ 4ᴀ2.
ɪᴠ. ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ᴄᴜʙᴏɪᴅ ᴏʀ ᴄᴜʙᴇ ᴍᴇᴀɴꜱ ᴛᴏᴛᴀʟ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ.
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