Question

Three cubes of metal whose edges are 6 cm 8 cm and 10 cm respectively are melted and a single cube is formed What is the length (in cm) of the diagonal of the newly formed cube?

• A. $10$
• B. $3\sqrt{10}$
• C. $12\sqrt{2}$
• D. $10\sqrt{2}$

Answer 1

The correct option is C $12\sqrt{2}$

Three cubes of metal whose edges are 6 cm 8 cm and 10 cm respectively are melted

Then volume of first cube =$(6{)}^3=216c{m}^3$

And volume of second cube =$(8{)}^3=512c{m}^3$

And volume of first cube =$(10{)}^3=1000c{m}^3$

Then volume of cube made by melted three cube=216+512+1000=1728

Then side of cube =$\sqrt{1728}=12$ cm

Then diagonal of cube =$\sqrt{3\times (12{)}^2}=12\sqrt{3}Cm$