If the length, breadth and height of a cuboid are increased such that the length is doubled, breadth becomes three times and the height becomes 4 times, find the ratio of to the new volume to the old.
Answers
Answer
Length of cuboid=l
Breadth of cuboid=b
Height of cuboid=h
Volume=lbh
Length of new cuboid =2l
Breadth of new cuboid= 1/2 b
Height of new cuboid=h
Volume = 2l × b/2 × h
Required ratio = lbh : 2l × 1/2 b × h
Height of new cuboid=h
Volume=2l× b/2 ×h
Required ratio=lbh:2l× 1/2 b × h
= lbh
⇒ ratio = Volume of original cuboid/Volume of new cuboid = lbh/lbh = 1
∴ ratio is 1⇒volume is the same. No change.
ʟᴇɴɢᴛʜ ᴏғ ᴄᴜʙᴏɪᴅ=ʟ
ʙʀᴇᴀᴅᴛʜ ᴏғ ᴄᴜʙᴏɪᴅ=ʙ
ʜᴇɪɢʜᴛ ᴏғ ᴄᴜʙᴏɪᴅ=ʜ
ᴠᴏʟᴜᴍᴇ=ʟʙʜ
ʟᴇɴɢᴛʜ ᴏғ ɴᴇᴡ ᴄᴜʙᴏɪᴅ =2ʟ
ʙʀᴇᴀᴅᴛʜ ᴏғ ɴᴇᴡ ᴄᴜʙᴏɪᴅ= 1/2 ʙ
ʜᴇɪɢʜᴛ ᴏғ ɴᴇᴡ ᴄᴜʙᴏɪᴅ=ʜ
ᴠᴏʟᴜᴍᴇ = 2ʟ × ʙ/2 × ʜ
ʀᴇϙᴜɪʀᴇᴅ ʀᴀᴛɪᴏ = ʟʙʜ : 2ʟ × 1/2 ʙ × ʜ
ʜᴇɪɢʜᴛ ᴏғ ɴᴇᴡ ᴄᴜʙᴏɪᴅ=ʜ
ᴠᴏʟᴜᴍᴇ=2ʟ× ʙ/2 ×ʜ
ʀᴇϙᴜɪʀᴇᴅ ʀᴀᴛɪᴏ=ʟʙʜ:2ʟ× 1/2 ʙ × ʜ
= ʟʙʜ
⇒ ʀᴀᴛɪᴏ = ᴠᴏʟᴜᴍᴇ ᴏғ ᴏʀɪɢɪɴᴀʟ ᴄᴜʙᴏɪᴅ/ᴠᴏʟᴜᴍᴇ ᴏғ ɴᴇᴡ ᴄᴜʙᴏɪᴅ = ʟʙʜ/ʟʙʜ = 1
∴ ʀᴀᴛɪᴏ ɪs 1⇒ᴠᴏʟᴜᴍᴇ ɪs ᴛʜᴇ sᴀᴍᴇ. ɴᴏ ᴄʜᴀɴɢᴇ.
ᴍᴀʀᴋ ɪᴛ ᴀs ʙʀᴀɪɴʟɪᴇsᴛ