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Surface Areas and Volumes — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsSurface Areas and Volumes1 Mark
MCQ
Three solid cubes have a face diagonal 4sqrt(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 length of an edge of the cube formed is
  • ✓
    12 cm
  • B
    24 cm
  • C
    18 cm
  • D
    26 cm
✓

Answer

Correct option: A.
12 cm
(a)
Let the lengths of edges of two sets of three cones each be a cm and b cm respectively. Then,
$\sqrt{2} a=4 \sqrt{2}$ and $\sqrt{2} b=8 \sqrt{2} \Rightarrow a=4$ and $b=8$
Let the length of an edge of new cube formed be c cm. Then,
$c^3=3 \times 4^3+3 \times 8^3=192+1536=1728=12^3 \Rightarrow c=12 cm$

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