Question

A cube and cuboid have the same volume. The dimensions of the cuboid are in the ratio of 1: 2: 4. If the difference between the cost of polishing the cuboid and the cube at the rate of Rs. 5 per m² is Rs. 80, find the edge of the cube.

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Answer 1

$\huge\fcolorbox{black}{aqua}{Solutioñ:-}$

⛄ Âղsաҽɾ:-

☘ ᴇᴅɢᴇ ᴏғ ᴛʜᴇ ᴄᴜʙᴇ = 4 ᴍ.

⛄ $Եҽթ-ճվ-sԵҽթ ҽxթlαղαԵíօղ:-

☘ ʟᴇᴛ ᴛʜᴇ ᴅɪᴍᴇɴsɪᴏɴs ᴏғ ᴛʜᴇ ᴄᴜʙᴏɪᴅ ʙᴇ x, 2x ᴀɴᴅ 4x ᴛʜᴇɴ ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ᴄᴜʙᴇ = ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ᴄᴜʙᴏɪᴅ

=) ᴀ³ = x × 2x × 4x

=) ᴀ³ = 8x³

ᴏʀ

→ ᴀ= 2x

↪ᴅɪғғᴇʀᴇɴᴄᴇ ɪɴ s.ᴀ. ᴏғ ᴄᴜʙᴏɪᴅ ᴀɴᴅ ᴄᴜʙᴇ

= s.ᴀ. ᴏғ ᴄᴜʙᴏɪᴅ - s.ᴀ. ᴏғ ᴄᴜʙᴇ

= 2(x × 2x + 2x × 4x + 4x × x) - 6(2x)²

= 2(2x² + 8x² + 4x²) - 6 × 4x²

= 28x² - 24x² = 4x²

ɴᴏᴡ,

↪ᴅɪғғᴇʀᴇɴᴄᴇ ɪɴ ᴄᴏsᴛ ᴏғ ᴘᴏʟɪsʜɪɴɢ

= 5 × 4x² = 20x² = 80

=) x² = 4

ᴏʀ,

→ x = 2ᴍ.

★ ᴛʜᴇʀᴇғᴏʀᴇ, ᴛʜᴇ ᴇᴅɢᴇ ᴏғ ᴛʜᴇ ᴄᴜʙᴇ ᴍᴇᴀsᴜʀᴇs:-

☞ 2x = 4ᴍ

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