Question

31) Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and

formed into a single cube. Find the edge of the cube so formed.​

Answer 1

ɢɪᴠᴇɴ, ᴇᴅɢᴇs ᴏғ ᴛʜʀᴇᴇ sᴏʟɪᴅ ᴄᴜʙᴇs ᴀʀᴇ 3 ᴄᴍ, 4 ᴄᴍ ᴀɴᴅ 5 ᴄᴍ, ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.

∴ ᴠᴏʟᴜᴍᴇ ᴏғ ғɪʀsᴛ ᴄᴜʙᴇ = (3)3 =

= 27 ᴄᴍ

ᴠᴏʟᴜᴍᴇ ᴏғ sᴇᴄᴏɴᴅ ᴄᴜʙᴇ = (4)3

= 64 ᴄᴍ3

ᴀɴᴅ ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜɪʀᴅ ᴄᴜʙᴇ = (5)3

= 125 ᴄᴍ3

∴ sᴜᴍ ᴏғ ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜʀᴇᴇ ᴄᴜʙᴇs = (27 + 64 + 125) = 216 ᴄᴍ3

ʟᴇᴛ ᴛʜᴇ ᴇᴅɢᴇ ᴏғ ᴛʜᴇ ʀᴇsᴜʟᴛɪɴɢ ᴄᴜʙᴇ = ʀ ᴄᴍ ᴛʜᴇɴ, ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ʀᴇsᴜʟᴛɪɴɢ ᴄᴜʙᴇ, ʀ3 =216 ⇒ ʀ = 6 ᴄᴍ.