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 form a cube. The side of the cube so formed is of length ___________.

Open in App
Solution

## We know that each face of a cube is a square. Let the side of solid cube having face diagonal of $4\sqrt{2}$ cm each be x cm. Diagonal of a square = $\sqrt{2}×\mathrm{Side}=\sqrt{2}x$ $\therefore \sqrt{2}x=4\sqrt{2}$ ⇒ x = 4 cm Now, let the side of solid cube having face diagonal of $8\sqrt{2}$ cm each be y cm. $\therefore \sqrt{2}y=8\sqrt{2}$ ⇒ y = 8 cm Suppose the side of the bigger cube obtained on melting the given cubes be a cm. ∴ Volume of the bigger cube = 3 × Volume of cube having side 4 cm + 3 × Volume of cube having side 8 cm $⇒{a}^{3}=3×{4}^{3}+3×{8}^{3}\phantom{\rule{0ex}{0ex}}⇒{a}^{3}=192+1536=1728\phantom{\rule{0ex}{0ex}}⇒{a}^{3}={\left(12\right)}^{3}\phantom{\rule{0ex}{0ex}}⇒a=12\mathrm{cm}$ 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 form a cube. The side of the cube so formed is of length __12 cm__.

Suggest Corrections
0
Related Videos
Cubes Relation with Cube Numbers
MATHEMATICS
Watch in App