Question

40 identical cubes each having edge 2 cm are melted to form a cuboid. If the cuboid has a square base and a height equivalent to 20 cm, find its total surface area.​

Answer 1

edge of cube = 2cm

height of cuboid (h) = 20cm

Since it has a square base

width (b) = length (l)

volume of cube = (edge)^3

                           = 2^3

                           = 8 cm^3

Volume of 40 cubes = 40(volume of cube)

                                    = 40 * 8

                                   = 320 cm^3

Volume of 40 cubes = Volume of cuboid

320 = lbh

       =20b^2

320/20 = b^2

b= √16

b = l = 4 cm

TSA of cuboid = 2(lb+bh+hl)

                        = 2(4*4 + 4*20 + 4*20)

                        = 2(16 + 80 + 80)

                        = 2(176)

                       = 352 cm^2