Three cubes of metal, of edges $6$ cm, $8$ cm and $10$ cm are melted to form a new cube. Find the diagonal of this new cube.

20.8

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50.8

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70.8

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None of these

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Solution

The correct option is A $20.8$ cm
As 3 cubes are melted to from a new cube
$\Rightarrow$ Vol. of 3 cube $=$ Vol of new cube
$\Rightarrow 6^{3} + 8^{3} + 10^{3} = a^{3} \Rightarrow a = 12$
diagonal of cube $- \sqrt{3} a = 12 \sqrt{3} = 20.8$

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Three cubes of metal, of edges 6 cm, 8 cm and 10 cm are melted to form a new cube. Find the diagonal of this new cube.

The correct option is A 20.8 cmAs 3 cubes are melted to from a new cube ⇒ Vol. of 3 cube = Vol of new cube ⇒63+83+103=a3⇒a=12diagonal of cube −√3a=12√3=20.8

Three cubes of metal, of edges $6$ cm, $8$ cm and $10$ cm are melted to form a new cube. Find the diagonal of this new cube.

The correct option is A $20.8$ cm
As 3 cubes are melted to from a new cube
$\Rightarrow$ Vol. of 3 cube $=$ Vol of new cube
$\Rightarrow 6^{3} + 8^{3} + 10^{3} = a^{3} \Rightarrow a = 12$
diagonal of cube $- \sqrt{3} a = 12 \sqrt{3} = 20.8$