Three solid cubes of sides $1$ cm, $6$ cm and $8$ cm respectively are melted to form a new cube. Find the surface area of the cube so formed.

520

sq. cm

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486

sq. cm

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289

sq. cm

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300

sq. cm

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Solution

The correct option is B $486$ sq. cm
The problem is solved by assuming total volume will not change
Final volume $=$ Initial volume
Cube 1 : $a_{1} = 1$ cm, $V_{1} = a_{1}^{3} = 1 c c$
Cube 2 : $a_{2} = 6$ cm, $V_{2} = a_{2}^{3} = 6^{3} = 216 c c$
Cube 3 : $a_{3} = 8$ cm, $V_{3} = a_{3}^{3} = 8^{3} = 512 c c$
Total volume $V = V_{1} + V_{2} + V_{3} = 1 + 216 + 512 = 9^{3}$
New side length $a = \sqrt[3]{V} = \sqrt[3]{729} = 9$ cm
Surface area of new cube $= 6 a^{2} = 6 \times 9^{2} = 6 \times 81 = 486$ sq. cm
Therefore, surface area of new cube = $486$ sq. cm

Option (B) is correct.

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Three solid cubes of sides 1 cm, 6 cm and 8 cm respectively are melted to form a new cube. Find the surface area of the cube so formed.

Three solid cubes of sides $1$ cm, $6$ cm and $8$ cm respectively are melted to form a new cube. Find the surface area of the cube so formed.