Three solid cubes have a face diagonal of 4-2 cm each- Three other solid cubes have a face diagonal of 8-2 cm each- All the cubes are melted together to from a big cube- Find the side of the cube formed in cm-

The correct option is B 12 Face of a cube is a square. Diagonal of a square = √(2)× side So, for Cube 1: √(2)× side_1 = 4 √(2) = gt; Sid ...

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Standard X

Mathematics

Shape Conversion of Solids

Three solid c...

Question

Three solid cubes have a face diagonal of $4 \sqrt{2}$ cm each. Three other solid cubes have a face diagonal of $8 \sqrt{2}$ cm each. All the cubes are melted together to from a big cube. Find the side of the cube formed (in cm).

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Solution

The correct option is B $12$
Face of a cube is a square.
Diagonal of a square $= \sqrt{2} \times s i d e$
So, for Cube 1:
$\sqrt{2} \times s i d e_{1} = 4 \sqrt{2}$
$=> S i d e_{1} = 4 c m$
And for Cube 2
$\sqrt{2} \times s i d e_{2} = 8 \sqrt{2}$
$=> S i d e_{2} = 8 c m$
So, total volume of all 6 cubes melted $= 3$ (Volume of cube_1) $+ 3$ (Volume of cube_2) $= 3 \times 4^{3} + 3 \times 8^{3} = 1728$ cu. cm.
As one large cube is formed with this volume, we have
(Side of large cube $)^{3} = 1728$
$\Rightarrow$ Side of large cube $= 12$ cm.

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Three solid cubes have a face diagonal of 4√2 cm each. Three other solid cubes have a face diagonal of 8√2 cm each. All the cubes are melted together to from a big cube. Find the side of the cube formed (in cm).

Three solid cubes have a face diagonal of $4 \sqrt{2}$ cm each. Three other solid cubes have a face diagonal of $8 \sqrt{2}$ cm each. All the cubes are melted together to from a big cube. Find the side of the cube formed (in cm).