Question

A cylinder, a cone and a hemisphere are equal base and the same height . What is the ratio of their volumes ?

Answer 1

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⎟⎟ ✪✪ ＱＵＥＳＴＩＯＮ ✪✪⎟⎟

ᴀ ᴄʏʟɪɴᴅᴇʀ, ᴀ ᴄᴏɴᴇ ᴀɴᴅ ᴀ ʜᴇᴍɪsᴘʜᴇʀᴇ ᴀʀᴇ ᴇϙᴜᴀʟ ʙᴀsᴇ ᴀɴᴅ ᴛʜᴇ sᴀᴍᴇ ʜᴇɪɢʜᴛ . ᴡʜᴀᴛ ɪs ᴛʜᴇ ʀᴀᴛɪᴏ ᴏғ ᴛʜᴇɪʀ ᴠᴏʟᴜᴍᴇs ?

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⎟⎟ ✿✿ ＡＮＳＷＥＲ ✿✿ ⎟⎟

★ Lᴇᴛ r ᴀɴᴅ h ʙᴇ ᴛʜᴇ ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ʙᴀsᴇ ᴀɴᴅ ʜᴇɪɢʜᴛ ᴏғ ᴄʏʟɪɴᴅᴇʀ, ᴄᴏɴᴇ ᴀɴᴅ ʜᴇᴍɪsᴘʜᴇʀᴇ.

Fᴏʀᴍᴜʟᴀ ᴜsɪɴɢ :-

ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ʜᴇᴍɪsᴘʜᴇʀᴇ = ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ʜᴇᴍɪsᴘʜᴇʀᴇ

★ ᴄʏʟɪɴᴅᴇʀ ★

➠ ᴠᴏʟᴜᴍᴇ = ᴄʏʟɪɴᴅᴇʀ

➠ πr²h = πr² × πr³

★ ᴄᴏɴᴇ ★

➠ ᴠᴏʟᴜᴍᴇ = ᴄᴏɴᴇ

➠ 1/3 πr²h = 1/3 πr² × 1/3 πr³

★ ʜᴇᴍɪsᴘʜᴇʀᴇ ★

➠ ᴠᴏʟᴜᴍᴇ = ʜᴇᴍɪsᴘʜᴇʀᴇ

➠ 2/3 πr³

Sᴏ ,

➞ πr³ : 1/3 πr³ : 2/3 πr³

➞ 1 : 1/3 : 2/3

➞ 3 : 1 : 2 ( ʙʏ ᴍᴜʟᴛɪᴘʟʏɪɴɢ ᴡɪᴛʜ 3 )

.°. ᴛʜᴇ ʀᴀᴛɪᴏ ᴏғ ᴛʜᴇɪʀ ᴠᴏʟᴜᴍᴇs ɪs 3 : 1 : 2

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