A well with 10 m inside diameter is dug 8m deep. earth is taken out of it and spread to form an embankment of 12 m width. Find the hight of the embankment.
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Answers
ɢɪᴠᴇɴ:
- ᴅᴇᴘᴛʜ ᴏғ ᴛʜᴇ ᴡᴇʟʟ, ʜ = 8.4ᴍ
- ɪɴsɪᴅᴇ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴡᴇʟʟ = 10ᴍ
- ᴡɪᴅᴛʜ ᴏғ ᴀɴ ᴇᴍʙᴀɴᴋᴍᴇɴᴛ. = 7.5 ᴍ
ᴛᴏ ғɪɴᴅ:
ᴛʜᴇ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴇᴍʙᴀɴᴋᴍᴇɴᴛ.
ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ʀᴀᴅɪᴜs ɪs ʜᴀʟғ ᴏғ ᴛʜᴇ ᴅɪᴀᴍᴇᴛᴇʀ.
ʜᴇɴᴄᴇ, ʀᴀᴅɪᴜs ʀ ᴏғ ᴡᴇʟʟ ᴄᴀɴ ʙᴇ ᴄᴀʟᴄᴜʟᴀᴛᴇᴅ ᴀs,
ʜᴇɴᴄᴇ, ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ᴡᴇʟʟ = 5ᴍ.
ɴᴏᴡ, ɪᴛ ɪs ᴀʟsᴏ ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴅᴇᴘᴛʜ ᴏғ ᴡᴇʟʟ ʜ = 8.4 ᴍ
ᴠᴏʟᴜᴍᴇ ᴏғ ᴇᴀʀᴛʜ ᴅᴜɢᴏᴜᴛ ᴄᴀɴ ʙᴇ ᴄᴀʟᴄᴜʟᴀᴛᴇᴅ ᴀs,
ᴠᴏʟᴜᴍᴇ ᴠ
ᴛʜᴜs, ᴡᴇ ʜᴀᴠᴇ ᴠᴏʟᴜᴍᴇ ᴏғ ᴇᴀʀᴛʜ ᴅᴜɢ ᴏᴜᴛ.
ᴡᴇ ᴀssᴜᴍᴇ ʜ' ɪs ᴛʜᴇ ʜᴇɪɢʜᴛ ᴏғ ᴇᴍʙᴀɴᴋᴍᴇɴᴛ
ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,
ɪɴɴᴇʀ ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ᴄʏʟɪɴᴅʀɪᴄᴀʟ sʜᴇʟʟ ɪs 5 ᴍ
ᴇxᴛᴇʀɴᴀʟ ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ᴄʏʟɪɴᴅʀɪᴄᴀʟ sʜᴇʟʟ ɪs 12.5ᴍ
ᴛʜᴇʀᴇғᴏʀᴇ, ᴡᴇ ᴄᴀɴ ᴡʀɪᴛᴇ ᴛʜᴇ ᴄᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ᴇᴍʙᴀʀᴋᴍᴇᴛ ᴀs,
ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ᴇᴍʙᴀɴᴋᴍᴇɴᴛ
ʙᴜᴛ, ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ᴇᴀʀᴛʜ ᴛʜᴀᴛ ᴡᴀs ᴅᴜɢᴏᴜᴛ ᴡɪʟʟ ʙᴇ sᴀᴍᴇ ᴀs ᴠᴏʟᴜᴍᴇ ᴏғ ᴇᴍʙᴀʀᴋᴍᴇɴᴛ
ᴛʜᴜs, ᴡᴇ ᴄᴀɴ ᴡʀɪᴛᴇ ᴛʜᴀᴛ ᴠᴏʟᴜᴍᴇ ᴏғ ᴇᴀʀᴛʜ ᴅᴜɢᴏᴜᴛ = ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ᴇᴍʙᴀɴᴋᴍᴇɴᴛ
ᴛʜᴇ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴇᴍʙᴀɴᴋᴍᴇɴᴛ ɪs 1.6ᴍ