Question

Three cubes of edge 3cm, 4cm, 5cm are melted to form a single cube . find the lateral surface area of the new cube ?

Answer 1

volume of a cube = cube root of sum of the edges of cubes
= a³+b³+c³
= 3³+4³+5³
= 27+64+125
= 216cm³

Edge of a new cube = ∛216 = 6cm

Lateral surface area of a cube = 4a² = 4*6*6 = 144cm²

Answer 2

volume of 1st cube=3 x 3 x3=27
volume of 2nd cube=4 x 4 x 4=64
volume of 3rd cube =5 x 5 x 5=125
therefore volume of new cube =27+64+125=216
                                      a³ =216
                                      a=6
 therefore lateral surface area of cube =4a²=4 x 36
                                                       =144 m² ans