If two cuboids of lengths 6 cm and 2 cm, breadths 2 cm and 1.5 cm and heights 2 cm and 1 cm are molten to form a single cube, find the side of the cube.

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Solution

$Under the given condition, Volume of {cuboid}_{1} + Volume of {cuboid}_{2} = Volume of the cube \Rightarrow ({length}_{1} \times {breadth}_{1} \times {height}_{1}) + ({length}_{2} \times {breadth}_{2} \times {height}_{2}) = {(side)}^{3} = (6 cm \times 2 cm \times 2 cm) + (2 cm \times 1.5 cm \times 1 cm) = 24 {cm}^{3} + 3 {cm}^{3} \Rightarrow {(Side)}^{3} = 27 {cm}^{3} \Rightarrow Side = 3 cm, since 3^{3} = 27$

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If two cuboids of lengths 6 cm and 2 cm, breadths 2 cm and 1.5 cm and heights 2 cm and 1 cm are molten to form a single cube, find the side of the cube.

Under the given condition,Volume of cuboid1+ Volume of cuboid2 = Volume of the cube⇒(length1×breadth1×height1) + (length2×breadth2×height2) = (side)3=(6 cm×2 cm×2cm) + (2 cm×1.5 cm×1 cm) =24 cm3 + 3 cm3 ⇒(Side)3 = 27 cm3⇒Side = 3 cm, since 33 = 27