Question

Three iron cubes of edge 3 cm, 4 cm and 5 cm respectively, are melted and cast into a single cube. Find the edge of the bigger cube formed.

• A. 9
• B. 10
• C. 6
• D. 8

Answer 1

The correct option is C

6

Volume of the cube 1 = $3cm\times 3cm\times 3cm$ = $27c{m}^3$

Volume of the cube 2 = $4cm\times 4cm\times 4cm$ = $64c{m}^3$

Volume of the cube 3 = $5cm\times 5cm\times 5cm$ = $125c{m}^3$

Thus total volume = $27c{m}^3+$ $64c{m}^3+$ $125c{m}^3$ = $216c{m}^3$

Let the edge of new cube to be x cm in length,

Volume of cube =$216c{m}^3$

$\Rightarrow x^3=216c{m}^3$

$\Rightarrow x=6cm$