Question

dimensions of a cuboid are 64 cm* 27 cm*8 cm.by how many square cm its total surface area is greater than the total surface area of a cube if equal volume.

Answer 1

first find total surface are of cuboid= 2(lb + bh + hl)
so l = 64 cm , b = 27 cm ,h = 8cm
so total surface are of cuboid = 2(64 x 27 + 27 x 8 + 8 x 64)
                                               = 2(2456) 
                                               = 4912 cm^2

and volume of cube = a1 x a2 x a3  = 13824 cm^3 
then
(side)a = cube root of 13824 = 24 cm
then total surface are of cube = 6(side)^2  = 6(44)^2 = 3456 cm^2

then 4912 - 3456 = 1456 cm^2,  total surface area of cuboid is greater than the total surface area of a cube.

regards 

Answer 2

Cuboid : 64 X 27 X 8 cm³
         Volume = 13,824 cm³
         T.S. A. = 2 (64*27+27*8 + 64 * 8) =  4,912 cm²

Side of the cube with equal volume of 13,824 cm³ = 24 cm.
       T.S. A . of cube = 6 * 24² = 3,456 cm²

Difference in T.S.A. = 4912 - 3456 = 1, 456 cm²