Three solid cubes of sides 3 cm, 4 cm and 5 cm are melted to form a new solid cube. Find the surface area (in cm²) of the cube so formed.

Correct option is C

Given:

Sides of three cubes are 3cm,4cm and 5cm

Formula Used:

Volume of cube = $$a^3$$​​

Total surface area of cube =$$6a^2$$​​

Solution:

Volume of cube with side 3cm =$$(3)^3 = 27cm^3$$​​

Volume of cube with side 4cm =$$(4)^3 = 64cm^3$$​​

Volume of cube with side 5cm =$$(5)^3 = 125cm^3$$​​

Total volume of the three cubes = 27 +64 +125 = 216$$cm^3$$​​

If the cubes are melted to form a new cube then volume remains same, hence

​$$a^3 = 216$$​​

​$$a=\sqrt[3]{216} =6cm$$​​

Total surface area to the new cube = $$6(6)^2 =216cm^3$$​​